Surface Areas and Volumes — Previous Year Questions (Class 10 Mathematics)
This chapter deals with surface areas and volumes of 3D shapes including cubes, cuboids, cylinders, cones, and spheres. Critical for real-world application
TL;DR: This chapter deals with surface areas and volumes of 3D shapes including cubes, cuboids, cylinders, cones, and spheres. Critical for real-world applic…
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This chapter deals with surface areas and volumes of 3D shapes including cubes, cuboids, cylinders, cones, and spheres. Critical for real-world application
Surface Areas and Volumes — Previous Year Questions with Solutions
Q (2023, 2 marks): Find the surface area of a cylinder with radius 7 cm and height 10 cm.
Answer: Surface area of cylinder = 2πr(r + h)
where r = 7 cm, h = 10 cm
SA = 2π(7)(7 + 10)
= 2π(7)(17)
= 2π(119)
= 238π cm²
≈ 238 × 22/7 = 748 cm²
Q (2022, 2 marks): A cone has base radius 5 cm and slant height 13 cm. Find its curved surface area.
Answer: Curved surface area of cone = πrl
where r = 5 cm, l = 13 cm
CSA = π(5)(13)
= 65π cm²
≈ 65 × 22/7 ≈ 204.29 cm²
Q (2023, 3 marks): A sphere has radius 6 cm. Find its surface area and volume.
Answer: Surface area = 4πr²
= 4π(6)²
= 4π(36)
= 144π cm²
≈ 452.39 cm²
Volume = (4/3)πr³
= (4/3)π(6)³
= (4/3)π(216)
= 288π cm³
≈ 904.78 cm³
Q (2021, 3 marks): A cuboid has dimensions 8 cm × 6 cm × 4 cm. Find its surface area and volume.
Answer: Surface area = 2(lw + wh + lh)
where l = 8, w = 6, h = 4
SA = 2(8×6 + 6×4 + 8×4)
= 2(48 + 24 + 32)
= 2(104)
= 208 cm²
Volume = l × w × h
V = 8 × 6 × 4
V = 192 cm³
Q (2022, 3 marks): A cone has height 12 cm and base radius 5 cm. Find its volume and slant height.
Answer: Slant height l = sqrt(h² + r²)
= sqrt(12² + 5²)
= sqrt(144 + 25)
= sqrt(169)
= 13 cm
Volume = (1/3)πr²h
= (1/3)π(5)²(12)
= (1/3)π(25)(12)
= 100π cm³
≈ 314.29 cm³
Q (2023, 2 marks): If the radius of a sphere is doubled, by what factor does its volume increase?
Answer: Original volume V1 = (4/3)πr³
New radius = 2r
New volume V2 = (4/3)π(2r)³ = (4/3)π(8r³) = 8 × (4/3)πr³ = 8V1
Volume increases by a factor of 8.
Frequently Asked Questions
What is the formula for lateral surface area of a cone?
The lateral (curved) surface area of a cone is πrl, where r is the base radius and l is the slant height. The total surface area includes the base: πrl + πr² = πr(l + r).
How are volume and surface area of a sphere related to radius?
Surface area = 4πr² (proportional to r²), Volume = (4/3)πr³ (proportional to r³). Doubling radius multiplies surface area by 4 and volume by 8.
More Class 10 Mathematics PYQs
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