Surface Areas and Volumes — Practice

Question 1

Find the CSA of a cylinder with radius 3.5 cm and height 10 cm. (Use π = 22/7.)

Accepted Answer

CSA = 2πrh = 2 × 22/7 × 3.5 × 10 = 220 cm².

Question 2

Find the volume of a sphere of radius 7 cm.

Accepted Answer

V = (4/3)πr³ = (4/3) × 22/7 × 343 = 4312/3 ≈ 1437.3 cm³.

Question 3

A cone has height 12 cm and radius 5 cm. Find its slant height and TSA.

Accepted Answer

ℓ = √(5² + 12²) = 13 cm. TSA = πr(r + ℓ) = π × 5 × 18 = 90π ≈ 282.86 cm².

Question 4

A solid is a cylinder (radius 7 cm, height 10 cm) with a hemisphere of the same radius on top. Find total surface area.

Accepted Answer

Exposed: cylinder's curved + cylinder's bottom + hemisphere's curved. = 2πr·h + πr² + 2πr² = 2π(7)(10) + π(49) + 2π(49) = 140π + 49π + 98π = 287π ≈ 901.71 cm².

Question 5

A metallic sphere of radius 10.5 cm is melted and recast into small cones of radius 3.5 cm and height 3 cm. How many cones?

Accepted Answer

V_sphere = (4/3)π(10.5)³ = 4851π cm³. V_cone = (1/3)π(3.5)²(3) = 12.25π cm³. Number = 4851π / 12.25π = 396 cones.

Practice — Surface Areas and Volumes

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