1
The total surface of a cuboid is —
💡 Hint:
Twice the paired faces.
Explanation:
2(lb + bh + hl).
Class 9 · Maths · Chapter 13 · बिहार बोर्ड (BSEB)CBSE · NCERT 2026-27
Surface Areas and Volumes
Surface Areas and Volumes
How to use this page:
1. Read — Exercise 13.1 · 13.2 · two cone activities · 13.3 · ball activity · 13.4 · 13.5 · 13.6 · cone-cylinder activity · 13.7 · 13.8 · 13.9, diagram, worked example, board tip
2. Check — each lesson has its own questions; the number follows the lesson
3. Mastery ★ — all of that lesson correct. Redo the wrong ones
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- 1 Surface of a cuboid and a cube
- 2 Surface of a cylinder
- 3 Cone surface and two activities
- 4 Sphere and hemisphere
- 5 Volume of a cuboid and a cube
- 6 Volume of a cylinder
- 7 Volume of a cone
- 8 Sphere volume and Exercises 13.8–13.9
- Chapter winner — every lesson at mastery ★
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📄 PDF download — notes + answer key
Surface of a cuboid and a cube
घनाभ और घन का पृष्ठ · Textbook 13.2 · Exercise 13.1
Six rectangles, or four wallsNotes
A cuboid has six faces. Total surface = 2(lb + bh + hl). The four walls are the lateral surface: 2h(l + b). If every edge of a cube is a, the total surface is 6a² and the lateral surface is 4a².
A box, paper or paint sits on this surface. For an overlap the book sometimes adds an extra percent of the total surface. If the paint is given in square metres, compare it with the surface, not with the volume.
Exercise 13.1Activity
This exercise asks for the surface of a cuboid and a cube. A sheet for a box, the four walls of a room, paint that covers a given square area, and a comparison of a cube with a cuboid. Keep lateral and total apart. The order is before the later cylinder exercise.
Worked exampleExample
Question: Find the total and the lateral surface of a 5 cm × 4 cm × 3 cm cuboid.
Formulas: total = 2(lb + bh + hl). Lateral = 2h(l + b).
Substitution: 2(20 + 12 + 15) = 2 × 47 = 94. Lateral = 2 × 3 × 9 = 54.
Unit: square centimetre.
10-second revision
- Total 2(lb+bh+hl)
- Four walls 2h(l+b)
- Cube 6a²
Board tip · BSEBBoard tip
Do not add the top and bottom faces in the lateral surface. They belong in the total.
Board tip · CBSEBoard tip
If the overlap is an extra 5%, first the whole surface, then 5% of it. Only 5% is not the answer.
Check your understandingall correct = mastery ★
2
The area of the four walls is 2h(l + b).
Explanation:
True — this is the lateral surface.
3
The total surface of a cube of edge 5 cm is ______ square centimetres.
💡 Hint:
6 × 25.
Explanation:
150 square centimetres.
4
If paint is given in square metres, compare it with —
💡 Hint:
Covering is a surface.
Explanation:
The surface.
5
Write the total and the lateral surface of 5 × 4 × 3 cm.
Model answer (board format)
Total = 2(20+12+15) = 94 square centimetres. Lateral = 2×3×(5+4) = 54 square centimetres.
Check your answer:
Surface of a cylinder
बेलन का पृष्ठ · Textbook 13.3 · Exercise 13.2
A paper rectangle wraps the cylinderNotes
Here a cylinder means a right circular cylinder unless something else is said. The length of the rectangle is the base circumference 2πr and the breadth is the height h. Curved surface = 2πrh. Add the two circular ends and the total = 2πr(r + h).
An open cylinder, such as a pipe, often asks only for the curved surface. A tin with lids asks for the total. Take π = 22/7 when the radius is a multiple of 7.
Exercise 13.2Activity
This exercise asks for the curved and the total surface of a cylinder. A road roller, a tin or a pipe comes after the cuboid in this order. Decide first whether it is open or closed.
Worked exampleExample
Question: r = 7 cm, h = 10 cm. Find the curved and the total surface. π = 22/7.
Formulas: curved = 2πrh. Total = 2πr(r + h).
Substitution: 2 × (22/7) × 7 × 10 = 440. 2 × (22/7) × 7 × 17 = 748.
Unit: square centimetre.
10-second revision
- Curved 2πrh
- Total 2πr(r+h)
- On 7 cm and 10 cm the values are 440 and 748
Board tip · BSEBBoard tip
In the total write r + h, not h alone. The base πr² is added twice.
Board tip · CBSEBoard tip
If π = 22/7 and r = 7, the 7 cancels. Show the cancel.
Check your understandingall correct = mastery ★
1
The curved surface of a cylinder is —
💡 Hint:
Circumference times height.
Explanation:
2πrh.
2
The total surface of a closed cylinder is 2πr(r + h).
Explanation:
True.
3
For r = 7 cm and h = 10 cm the curved surface is ______ square centimetres. π = 22/7.
💡 Hint:
2×22×10.
Explanation:
440 square centimetres.
4
Why is the total surface of that cylinder 748? Write the formula and the substitution.
Model answer (board format)
2πr(r+h) = 2×(22/7)×7×17 = 748 square centimetres.
Check your answer:
Cone surface and two activities
शंकु का पृष्ठ और दो गतिविधियाँ · Textbook 13.4 · Exercise 13.3
The slant from PythagorasNotes
Rotate a right triangle about one perpendicular side and a cone appears. This is the book’s first unnumbered activity. Open a paper cone and a sector appears. The cut line is the slant l. This is the second activity.
l = √(r² + h²). Curved surface = πrl. Total = πr(l + r). The cloth of a tent is often the curved surface. The circle on the ground is added separately.
Exercise 13.3Activity
After the two activities, Exercise 13.3 asks for the surface of a cone. For a cap or a tent, find l first. The curved and the total surfaces are different answers.
Worked exampleExample
Question: r = 7 cm, h = 24 cm. Find l, the curved surface and the total surface. π = 22/7.
Formulas: l = √(r² + h²). Curved = πrl. Total = πr(l + r).
Substitution: l = √(49 + 576) = √625 = 25 cm. Curved = (22/7)×7×25 = 550. Total = (22/7)×7×32 = 704.
Units: centimetre and square centimetre.
10-second revision
- l = √(r²+h²)
- Curved πrl, total πr(l+r)
- On 7 and 24, l = 25
Board tip · BSEBBoard tip
Do not write h in the curved surface. First show l = 25, then πrl.
Board tip · CBSEBoard tip
Both activities are unnumbered. Do not turn them into 13.1.
Check your understandingall correct = mastery ★
1
The slant l equals —
💡 Hint:
A right triangle.
Explanation:
√(r² + h²).
2
The curved surface of a cone is πrl.
Explanation:
True.
3
For r = 7 and h = 24 cm, l = ______ cm.
💡 Hint:
√625.
Explanation:
25 cm.
4
When a paper cone is opened, the cut is —
💡 Hint:
The second activity.
Explanation:
The slant l.
5
r = 7 cm, h = 24 cm, π = 22/7. Write the curved surface.
Model answer (board format)
l = 25 cm. πrl = (22/7)×7×25 = 550 square centimetres.
Check your answer:
6
The total surface of a cone does not add the base.
Explanation:
False — total = πr(l + r), so the base πr² is included.
Sphere and hemisphere
गोला और अर्धगोला · Textbook 13.5 · Exercise 13.4
String on a ball, surface 4πr²Notes
Rotate a circle and a sphere appears. The book gives an unnumbered activity of winding string on a ball. A sphere is the surface. The solid ball is called a solid sphere. Surface = 4πr².
The curved surface of a hemisphere is 2πr². Add the base circle and the total is 3πr². Paint a bowl on the inside and you want the curved surface. A toy with a lid wants the total.
Exercise 13.4Activity
After the string activity, Exercise 13.4 asks for the surface of a sphere and a hemisphere. The radius is half the diameter. The surface depends on r², not on r.
Worked exampleExample
Question: r = 7 cm. Write the sphere surface and the curved and total surfaces of a hemisphere. π = 22/7.
Formulas: sphere 4πr². Hemisphere curved 2πr². Hemisphere total 3πr².
Substitution: 4×(22/7)×49 = 616. Curved = 308. Total = 462.
Unit: square centimetre.
10-second revision
- Sphere 4πr²
- Hemisphere curved 2πr²
- Hemisphere total 3πr²
Board tip · BSEBBoard tip
The total surface of a hemisphere is not 2πr². The base joins and it becomes 3πr².
Board tip · CBSEBoard tip
If the diameter is 14 cm, write r = 7 cm first. Do not put 14 straight into the formula.
Check your understandingall correct = mastery ★
1
The surface of a sphere is —
💡 Hint:
Volume comes later.
Explanation:
4πr².
2
The total surface of a hemisphere is 3πr².
Explanation:
True — curved 2πr² and base πr².
3
For r = 7 cm the sphere surface is ______ square centimetres.
💡 Hint:
4×22×7.
Explanation:
616 square centimetres.
4
If the diameter is 14 cm, the radius is —
💡 Hint:
Half.
Explanation:
7 cm.
5
Write the curved and total surfaces of a hemisphere for r = 7 cm.
Model answer (board format)
Curved = 2×(22/7)×49 = 308 square centimetres. Total = 3×(22/7)×49 = 462 square centimetres.
Check your answer:
Volume of a cuboid and a cube
घनाभ और घन का आयतन · Textbook 13.6 · Exercise 13.5
Space in cubic unitsNotes
Volume is the space occupied. Capacity is the inside of a hollow container. Volume of a cuboid = l × b × h. Volume of a cube is a³.
The unit is the cubic centimetre or the cubic metre. 1 m³ = 1000000 cm³, because each edge is 100 cm and 100³ is one million. Do not repeat a surface formula here.
Exercise 13.5Activity
After the four surface exercises, this is the first volume exercise. The space of a cuboid and a cube, and capacity. The answer will be in cubic units.
Worked exampleExample
Question: Find the volume of 5 cm × 4 cm × 3 cm and of a cube of edge 10 cm.
Formulas: V = lbh. Cube V = a³.
Substitution: 5 × 4 × 3 = 60. 10³ = 1000.
Unit: cubic centimetre.
10-second revision
- V = lbh
- Cube a³
- 1 m³ = 10⁶ cm³
Board tip · BSEBBoard tip
Write cubic centimetres with 60. Square centimetres are not a volume answer.
Board tip · CBSEBoard tip
If metres and centimetres are mixed, use one unit first. 1 m = 100 cm.
Check your understandingall correct = mastery ★
1
The volume of a cuboid is —
💡 Hint:
The product of three measures.
Explanation:
lbh.
2
1 cubic metre = 1000000 cubic centimetres.
Explanation:
True — 100³ = 1000000.
3
The volume of 5 × 4 × 3 cm is ______ cubic centimetres.
💡 Hint:
5×4×3.
Explanation:
60 cubic centimetres.
4
Write both the surface and the volume of a cube of edge 10 cm, with separate units.
Model answer (board format)
Surface = 6×100 = 600 square centimetres. Volume = 1000 cubic centimetres.
Check your answer:
Volume of a cylinder
बेलन का आयतन · Textbook 13.7 · Exercise 13.6
Base area times heightNotes
Volume of a cylinder = πr²h. This is the area of the base circle times the height. It is different from the surface 2πrh. The r is squared, not the h.
The capacity of a well, a pipe or a tank is this volume. If the metal has thickness, the metal is the difference of the outer and inner volumes. Exercise 13.6 is the volume turn after the surface exercise 13.2.
Exercise 13.6Activity
The number is 13.6, because 13.5 was the cuboid volume. Here a cylinder is filled. Keep the answer in cubic units. If π = 22/7 and r = 7, the arithmetic is short.
Worked exampleExample
Question: r = 7 cm, h = 10 cm. Find the volume. π = 22/7.
Formula: V = πr²h.
Substitution: (22/7) × 49 × 10 = 1540.
Unit: cubic centimetre.
10-second revision
- V = πr²h
- Square the r, not the h
- On 7 and 10 the volume is 1540
Board tip · BSEBBoard tip
2πrh is not the volume. It is the curved surface. Write πr²h.
Board tip · CBSEBoard tip
If there is thickness, subtract the two volumes. Do not take one average radius.
Check your understandingall correct = mastery ★
1
The volume of a cylinder is —
💡 Hint:
Base times height.
Explanation:
πr²h.
2
Exercise 13.6 is the volume of a cylinder, not the surface.
Explanation:
True — the surface was in 13.2.
3
For r = 7 cm, h = 10 cm and π = 22/7 the volume is ______ cubic centimetres.
💡 Hint:
22×7×10.
Explanation:
1540 cubic centimetres.
4
The volume of the metal thickness is —
💡 Hint:
The difference.
Explanation:
Outer minus inner.
5
Find the volume for r = 7 cm and h = 5 cm. π = 22/7.
Model answer (board format)
πr²h = (22/7)×49×5 = 770 cubic centimetres.
Check your answer:
6
The volume does not square r.
Explanation:
False — πr²h squares r.
Volume of a cone
शंकु का आयतन · Textbook 13.8 · Exercise 13.7
Three cones, one cylinderNotes
Make a hollow cone and a hollow cylinder of the same r and h. This is the book’s next unnumbered activity, after the ball activity. Three cones fill the cylinder. Volume of a cone = (1/3)πr²h.
Here h is the height, not l. A heap of sand or grain is a cone. Exercise 13.7 is on this volume.
Exercise 13.7Activity
After the activity, Exercise 13.7 asks you to fill a cone. Write the 1/3. The matching cylinder has three times the volume.
Worked exampleExample
Question: r = 7 cm, h = 24 cm. Find the volume of the cone. π = 22/7.
Formula: V = (1/3)πr²h.
Substitution: (1/3) × (22/7) × 49 × 24 = (1/3) × 3696 = 1232.
Unit: cubic centimetre.
10-second revision
- V = (1/3)πr²h
- Three cones = one cylinder
- On 7 and 24 the volume is 1232
Board tip · BSEBBoard tip
Do not put l = 25 into the volume. The volume uses h = 24.
Board tip · CBSEBoard tip
Forgetting 1/3 gives 3696. That is the cylinder, not the cone.
Check your understandingall correct = mastery ★
1
The volume of a cone is —
💡 Hint:
A third of the cylinder.
Explanation:
(1/3)πr²h.
2
For the same r and h, three cones fill one cylinder.
Explanation:
True — that is the activity.
3
For r = 7 cm and h = 24 cm the cone volume is ______ cubic centimetres.
💡 Hint:
3696 ÷ 3.
Explanation:
1232 cubic centimetres.
4
The volume uses —
💡 Hint:
l belongs to the surface.
Explanation:
The height h.
5
What is the volume of the matching cylinder? Give the reason.
Model answer (board format)
The cylinder = 3 × 1232 = 3696 cubic centimetres, because the cone is one third of it.
Check your answer:
Sphere volume and Exercises 13.8–13.9
गोले का आयतन और अभ्यास 13.8–13.9 · Textbook 13.9 · Exercise 13.8 · optional 13.9
Overflowing water shows the volumeNotes
Dip a sphere in water and the overflow is about (4/3)πr³. Volume of a sphere = (4/3)πr³. The volume of a hemisphere is half of that, (2/3)πr³. The air inside a dome is volume, and the whitewash is surface.
Exercise 13.8 asks for this. Exercise 13.9 is optional and, as the book says, not for the examination. It has the paint on a bookshelf, wooden spheres on supports, and the percent fall in curved surface when the diameter falls 25%. The fall is 43.75%.
Exercise 13.8 and optional 13.9Activity
13.8 is the volume of a sphere and a hemisphere, including a capsule and a dome. 13.9 is last. Do not do it before 13.8 and do not change the number. In the 25% fall, the new r is 3/4 of the old. The surface ratio is (3/4)² = 9/16.
Worked exampleExample
Question: If the diameter falls by 20%, by what percent does the curved surface fall?
Formula: new surface / old surface = (new radius / old radius)².
Substitution: the ratio is 0.8. 0.8² = 0.64. Fall = 1 − 0.64 = 0.36 = 36%.
Unit: percent.
10-second revision
- Sphere (4/3)πr³
- Hemisphere (2/3)πr³
- A 25% fall cuts the surface by 43.75%
Board tip · BSEBBoard tip
On a dome the whitewash is the curved surface 2πr², and the air is (2/3)πr³. They are not one answer.
Board tip · CBSEBoard tip
Do not write 13.9 as a compulsory examination question. The book calls it optional.
Check your understandingall correct = mastery ★
1
The volume of a sphere is —
💡 Hint:
The cubic power.
Explanation:
(4/3)πr³.
2
Exercise 13.9 is optional.
Explanation:
True — the book says it is not for the examination.
3
If the diameter falls 25%, the curved surface falls by ______ percent.
💡 Hint:
7/16 × 100.
Explanation:
43.75%.
4
Write the volume of a sphere of r = 7 cm from (4/3)πr³. π = 22/7.
Model answer (board format)
(4/3)×(22/7)×343 = (4/3)×22×49 = 4312/3 cubic centimetres.
Check your answer:
❓ Full question bank — with answers and explanations — 66 questions
Pick a type. The 39 lesson checks are separate — each lesson has as many as its topic needs. All correct earns mastery ★.
BSEB modelpractice · not annual60 tried · 0 correctMultiple choiceMCQ130 tried · 0 correctTrue / falseTrue / false80 tried · 0 correctFill in the blanksFill80 tried · 0 correctMatchMatch20 tried · 0 correctAssertion–reasonAssertion–reason50 tried · 0 correctBalancingBalancing40 tried · 0 correctIdentifyIdentify20 tried · 0 correctShort and longVSA, SA, LA120 tried · 0 correctCBSE-stylenot a PYQ60 tried · 0 correct
No question is marked as a verified past paper. The BSEB set is a model for practice. CBSE items are CBSE-style, not a copy of any year’s paper.
Multiple choice
0/13Pick one option. A wrong try brings a hint.
1
The total surface of a cuboid is —
💡 Hint:
Six faces.
Explanation:
2(lb+bh+hl).
2
The total surface of a cube is —
💡 Hint:
Six squares.
Explanation:
6a².
3
The curved surface of a cylinder is —
💡 Hint:
Circumference × height.
Explanation:
2πrh.
4
The total surface of a cylinder is —
💡 Hint:
Two bases join.
Explanation:
2πr(r+h).
5
The slant of a cone is —
💡 Hint:
Pythagoras.
Explanation:
√(r²+h²).
6
The curved surface of a cone is —
💡 Hint:
l is the slant.
Explanation:
πrl.
7
The surface of a sphere is —
💡 Hint:
The whole sphere.
Explanation:
4πr².
8
The total surface of a hemisphere is —
💡 Hint:
Curved plus base.
Explanation:
3πr².
9
The volume of a cylinder is —
💡 Hint:
Base × height.
Explanation:
πr²h.
10
The volume of a cone is —
💡 Hint:
Three cones make one cylinder.
Explanation:
(1/3)πr²h.
11
The volume of a sphere is —
💡 Hint:
Cubic power.
Explanation:
(4/3)πr³.
12
If the diameter falls 25%, the curved surface falls by —
💡 Hint:
(3/4)² = 9/16.
Explanation:
43.75%.
13
The four walls are —
💡 Hint:
Lateral surface.
Explanation:
2h(l+b).
True or false
0/81
The curved surface of a cylinder is πr²h.
Explanation:
False — that is the volume. The curved surface is 2πrh.
2
The curved surface of a cone uses the slant l.
Explanation:
True — πrl.
3
The curved surface of a hemisphere is 3πr².
Explanation:
False — the curved surface is 2πr². 3πr² is the total.
4
1 m³ = 1000000 cm³.
Explanation:
True.
5
Three matching cones fill one matching cylinder.
Explanation:
True.
6
Exercise 13.9 is written as compulsory for the examination.
Explanation:
False — the book calls it optional.
7
Capacity is the space inside a hollow container.
Explanation:
True.
8
The diameter can be written straight in place of r in 4πr².
Explanation:
False — halve it first.
Fill in the blanks
0/81
The total surface of a 5×4×3 cuboid is ______ square centimetres.
💡 Hint:
2×47.
Explanation:
94.
2
For r = 7 and h = 10 the cylinder curved surface is ______.
💡 Hint:
2×22×10.
Explanation:
440.
3
For r = 7 and h = 24 the slant l is ______ cm.
💡 Hint:
√625.
Explanation:
25.
4
For r = 7 the sphere surface is ______.
💡 Hint:
4×22×7.
Explanation:
616.
5
The volume of 5×4×3 is ______ cubic centimetres.
💡 Hint:
Multiply.
Explanation:
60.
6
For r = 7 and h = 10 the cylinder volume is ______.
💡 Hint:
22×70.
Explanation:
1540.
7
The cone with that r and h = 24 has volume ______.
💡 Hint:
3696/3.
Explanation:
1232.
8
If the diameter falls 20%, the surface falls by ______ percent.
💡 Hint:
1−0.64.
Explanation:
36.
Match
0/21
Match the solid with its curved or whole surface.
Column B: A. 3πr² · B. 2πrh · C. πrl · D. 4πr²
1. Cylinder curved
2. Cone curved
3. Sphere
4. Hemisphere total
Explanation:
Cylinder 2πrh, cone πrl, sphere 4πr², hemisphere total 3πr².
2
Match the exercise with its solid.
Column B: A. Sphere volume · B. Cuboid surface · C. Cone surface · D. Cone volume
1. 13.1
2. 13.3
3. 13.7
4. 13.8
Explanation:
13.1 is cuboid surface, 13.3 cone surface, 13.7 cone volume, and 13.8 sphere volume.
Assertion–reason
0/5Check both statements, then see whether the reason explains the assertion.
1
Assertion (A): The curved surface of a cone is πrl.
Reason (R): l = √(r² + h²) is the slant.
Explanation:
Both are true and R says what l is.
2
Assertion (A): The volume of a cylinder is πr²h.
Reason (R): The surface of a sphere is 4πr².
Explanation:
Both are true, but R does not explain the volume.
3
Assertion (A): Three cones fill one matching cylinder.
Reason (R): So the cone volume is 3πr²h.
Explanation:
A is true. R is false — the volume is (1/3)πr²h.
4
Assertion (A): The curved surface of a hemisphere is 3πr².
Reason (R): The total surface of a hemisphere is 3πr².
Explanation:
A is false. R is true. The curved surface is 2πr².
5
Assertion (A): If the diameter falls 25%, the curved surface falls 43.75%.
Reason (R): Surface depends on the square of the radius and the new radius is 3/4.
Explanation:
Both are true and R is the reason. 1 − 9/16 = 7/16.
Coefficient practice
0/4These are not results of this maths chapter. They are only coefficient practice for H2 + O2 → H2O.
1
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). This is not a volume result.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
2
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). Match the hydrogen count.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
3
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). Match the oxygen count.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
4
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). A blank coefficient is 1.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
Classify
0/21
Place each formula under surface or volume.
2πrh
πr²h
4πr²
(4/3)πr³
Explanation:
2πrh and 4πr² are surfaces. πr²h and (4/3)πr³ are volumes.
2
Place each exercise in its place.
Cuboid surface
Cuboid volume
Optional last exercise
Cylinder surface
Explanation:
Surfaces are 13.1 and 13.2. Volume is 13.5. Optional is 13.9.
Very short answer
0/51
Write the total surface of a cuboid.
Model answer (board format)
2(lb + bh + hl).
Check your answer:
2
Write l and the curved surface of a cone.
Model answer (board format)
l = √(r²+h²). Curved = πrl.
Check your answer:
3
Write the surface and the volume of a sphere.
Model answer (board format)
Surface 4πr². Volume (4/3)πr³.
Check your answer:
4
Write the volume of a hemisphere.
Model answer (board format)
(2/3)πr³.
Check your answer:
5
Write the formula for four walls.
Model answer (board format)
2h(l + b).
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Short answer
0/41
r = 7 cm, h = 10 cm, π = 22/7. Write the cylinder curved surface and volume.
Model answer (board format)
Curved = 440 square centimetres. Volume = 1540 cubic centimetres.
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2
r = 7, h = 24. Write l and the cone volume.
Model answer (board format)
l = 25 cm. Volume = 1232 cubic centimetres. π = 22/7.
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3
Write the curved surface and the volume of a hemisphere of r = 7 cm.
Model answer (board format)
Curved = 308 square centimetres. Volume = (2/3)×(22/7)×343 = 2156/3 cubic centimetres.
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4
Show the percent fall in curved surface when the diameter falls 25%.
Model answer (board format)
New/old = (3/4)² = 9/16. Fall = 7/16 = 43.75%.
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Long answer
0/31
Write the surface formulas of a cuboid, a cylinder, a cone and a sphere. Also find the total surface of 5×4×3.
Model answer (board format)
2(lb+bh+hl), 2πrh and 2πr(r+h), πrl and πr(l+r), 4πr². The total of 5×4×3 = 94 square centimetres.
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2
Write four volume formulas. Find the volume of the cylinder r = 7, h = 10 and of the sphere r = 7. π = 22/7.
Model answer (board format)
lbh, πr²h, (1/3)πr²h, (4/3)πr³. Cylinder 1540 cubic centimetres. Sphere 4312/3 cubic centimetres.
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3
Which solid is each of Exercises 13.1 to 13.9 about? Write one caution about 13.9.
Model answer (board format)
13.1 cuboid-cube surface. 13.2 cylinder surface. 13.3 cone surface. 13.4 sphere surface. 13.5 cuboid volume. 13.6 cylinder volume. 13.7 cone volume. 13.8 sphere volume. 13.9 is optional, not for the examination.
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BSEB model paper · practice
0/6This model set is for practice. It is not a question from any year’s annual examination. Annual questions will be added only when a source page is available.
1
The lateral surface 2h(l+b) belongs to —
💡 Hint:
Four walls.
Explanation:
A cuboid.
2
1232 cubic centimetres is the volume of which cone when π = 22/7?
💡 Hint:
(1/3)πr²h.
Explanation:
r = 7 cm, h = 24 cm.
3
The surface of a cube of edge 5 cm is ______ square centimetres.
💡 Hint:
6×25.
Explanation:
150.
4
The whitewash of a dome is volume.
Explanation:
False — whitewash is surface. The air inside is volume.
5
Write both the curved surface and the volume of the cone r = 7 cm, h = 24 cm.
Model answer (board format)
l = 25 cm. Curved = 550 square centimetres. Volume = 1232 cubic centimetres.
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6
This is coefficient practice, not a result of surface or volume. Balance H2 + O2 making H2O by filling coefficients (blank = 1).
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
CBSE-style questions
0/6These are competency-based practice questions. They are not copies of a CBSE paper.
1
A student writes 2πr(r+h) for an open pipe. An open pipe asks for —
💡 Hint:
There is no lid.
Explanation:
2πrh.
2
A heap of sand is a cone. Its volume uses —
💡 Hint:
Height h.
Explanation:
(1/3)πr²h.
3
Assertion (A): The capacity of a tank is a volume.
Reason (R): Paint is also measured in that cubic unit.
Explanation:
A is true. R is false — paint asks for the square unit of a surface.
4
A diameter of 14 cm means r = 14 cm.
Explanation:
False — r = 7 cm.
5
A water tank is a cylinder, r = 7 m and h = 2 m. Write the capacity in cubic metres. π = 22/7. Why is this not paint?
Model answer (board format)
V = (22/7)×49×2 = 308 cubic metres. Paint is surface. Capacity is volume.
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6
A ball has diameter 14 cm. Find the surface and say what the string activity measures.
Model answer (board format)
r = 7 cm. Surface = 616 square centimetres. The string measures surface, not volume.
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🏛️ Board exam corner — Bihar Board (BSEB)— CBSE
Switch board with BSEB | CBSE above. The lessons follow the same NCERT chapter.
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This page has no verified annual-exam question, because no source page has been added. The model set below is practice in the board pattern.
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CBSE-style · competency-based
These are case and assertion-reason practice items. Do not treat them as past CBSE questions.
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🧠 What you learned + equation sheet
What you learned
- The total surface of a cuboid is 2(lb + bh + hl) and of a cube is 6a².
- The curved surface of a cylinder is 2πrh and the total is 2πr(r + h).
- In a cone l = √(r² + h²), the curved surface is πrl and the total is πr(l + r).
- The surface of a sphere is 4πr². A hemisphere has curved surface 2πr² and total surface 3πr².
- Volumes: cuboid lbh, cylinder πr²h, cone (1/3)πr²h, sphere (4/3)πr³.
- Exercise 13.9 is optional. If the diameter falls 25%, the curved surface falls 43.75%.
| What | Keep this |
|---|---|
| Cuboid surface | 2(lb+bh+hl) |
| Cylinder CSA | 2πrh |
| Cone slant | l = √(r²+h²) |
| Sphere surface | 4πr² |
| Cone volume | (1/3)πr²h |
| Sphere volume | (4/3)πr³ |
The notes are original writing. The textbook was used only for activity order and numbers. “Verified” will be used only on a question that has a source page.