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CBSE · Class 10 · Mathematics

Surface Areas and Volumes

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
A solid is a cylinder of radius 7 cm and height 15 cm with a hemisphere of the same radius on top. Its volume (π = 22/7) is:
  1. 3,747 1/3 cm3
  2. 2,310 cm3
  3. 3,050 2/3 cm3
  4. 3,028 2/3 cm3
2.
A paperweight is a cone of radius 105 cm and slant height 111 cm mounted on a hemisphere of the same radius. Its total surface area (π = 22/7) is:
  1. 140,580 cm2
  2. 36,630 cm2
  3. 105,930 cm2
  4. 175,230 cm2
3.
A solid is a cube of edge 28 cm with a hemisphere of diameter 28 cm fixed on top. Its surface area (π = 22/7) is:
  1. 6,320 cm2
  2. 4,704 cm2
  3. 5,320 cm2
  4. 5,936 cm2
4.
A capsule is a cylinder 36 mm long with a hemisphere of radius 7 mm at each end. Its surface area (π = 22/7) is:
  1. 1,892 mm2
  2. 1,584 mm2
  3. 2,200 mm2
  4. 2,508 mm2
5.
The curved surface area of a cylinder of radius r and height h is:
  1. 2πrh
  2. πrh
  3. πr2h
  4. 2πr(r + h)
6.
A solid is a cylinder of radius 14 cm and height 33 cm with a cone of the same radius and height 22 cm on top. Its volume (π = 22/7) is:
  1. 25,845 1/3 cm3
  2. 33,880 cm3
  3. 20,328 cm3
  4. 24,845 1/3 cm3
7.
A cone of the same base and height is carved out of a solid cylinder of radius 7 cm and height 23 cm. The volume left (π = 22/7) is:
  1. 2,361 1/3 cm3
  2. 3,361 1/3 cm3
  3. 1,180 2/3 cm3
  4. 3,542 cm3
8.
Assertion (A): A toy made of a cone (radius 21 cm, slant height 29 cm) on a hemisphere of the same radius has a surface area of 4,686 cm2 (π = 22/7).
Reason (R): The surface area of a combined solid is the sum of the total surface areas of its parts.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
A tent is a cylinder of radius 7 m and height 14 m with a cone of the same radius and slant height 25 m on top. Find the area of canvas used (π = 22/7).
10.
An ice-cream cone is a cone of radius 42 mm and height 56 mm, filled with ice-cream and topped with a hemisphere of the same radius. Find the volume of ice-cream (π = 22/7).
11.
A capsule is a cylinder 32 mm long with a hemisphere of radius 14 mm at each end. Find its volume (π = 22/7).
12.
A buoy is a cone standing on a hemisphere, both of radius 14 cm, and the height of the cone equals its radius. Find its volume (π = 22/7).
13.
A hemispherical hollow of radius 7 cm is scooped out of the top of a solid wooden block 33 cm × 32 cm × 15 cm. Find the volume of wood left (π = 22/7).
14.
A container is a cylinder of radius 7 cm and height 23 cm, but its bottom is a raised hemisphere of the same radius. Find how much it seems to hold and how much it really holds (π = 22/7).
15.
A bird bath is a cylinder of radius 42 cm and height 140 cm with a hemispherical bowl of the same radius at the top. Find its total surface area, outside of the cylinder and inside of the bowl (π = 22/7).
16.
A solid is a cylinder of radius 14 cm and height 35 cm with a cone of the same radius and slant height 50 cm on top. Find its total surface area (π = 22/7).
Section C — Word problems4 × 4 = 16 marks
17.
A circus tent is a cylinder of radius 35 m and height 7 m with a cone of slant height 37 m on top. Find the cost of the canvas at Rs 63 per m2 (π = 22/7).
18.
A toy is a cone of radius 42 mm and height 144 mm on a hemisphere of the same radius. A cylinder is drawn around it, touching it. Find the difference between the volume of the cylinder and the toy (π = 22/7).
19.
A storage tank is a cylinder of radius 7 m and height 12 m with a hemispherical bottom of the same radius. How much can it hold (π = 22/7)?
20.
A solid iron pole is a cylinder of radius 14 cm and height 110 cm with a cylinder of radius 7 cm and height 80 cm on top. Iron has a mass of 8 g per cm3. Find the mass of the pole (π = 22/7).
AmbifulWorksheets
Practice that never repeats
CBSE · Class 10 · Mathematics

Answer key

Surface Areas and Volumes · AW-10M-SAV-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 3,028 2/3 cm3πr2h + (2/3)πr3 = 2,310 + 718 2/3
2(c) 105,930 cm2πrl + 2πr2 = 36,630 + 69,300
3(c) 5,320 cm26a2 − πr2 + 2πr2 = 6a2 + πr2 = 4,704 + 616
4(c) 2,200 mm22πrh + 4πr2 = 1,584 + 616
5(a) 2πrh—
6(d) 24,845 1/3 cm3πr2h1 + (1/3)πr2h2 = 20,328 + 4,517 1/3
7(a) 2,361 1/3 cm3πr2h − (1/3)πr2h = (2/3)πr2h
8(c) A is true, but R is false.A is true: πrl + 2πr2 = 4,686. R is false.
91,166 m22πrh + πrl = 616 + 550
10258,720 mm3(1/3)πr2h + (2/3)πr3 = 103,488 + 155,232
1131,210 2/3 mm3πr2h + (4/3)πr3 = 19,712 + 11,498 2/3
128,624 cm3(1/3)πr3 + (2/3)πr3 = πr3 = 22/7 × 143
1315,121 1/3 cm315,840 − (2/3) × 22/7 × 73 = 15,840 − 718 2/3
14seems 3,542 cm3; really 2,823 1/3 cm3apparent πr2h; actual πr2h − (2/3)πr3
1548,048 cm22πrh + 2πr2 = 36,960 + 11,088
165,896 cm2base πr2 + 2πrh + πrl
17Rs 353,430canvas = 2πrh + πrl = 5,610 m2
18609,840 mm3cylinder 1,031,184 (height 186); toy 421,344
192,566 2/3 m3πr2h + (2/3)πr3 = 1,848 + 718 2/3
20640.64 kgvolume = 80,080 cm3; mass = 80,080 × 8 g