Question

If the volume of a cylinder is 16π cm3 with radius of 2 cm, what is the surface area of the cylinder? (in terms of π)

A) 12π cm2
B) 24π cm2
C) 32π cm2
D) 36π cm2

Answer 1

36π cm∧2

Explanation:

Answer 2

Option B

Surface area of cylinder is 24π square centimeter

Solution:

Given that volume of a cylinder is
`16\pi` cubic centimeter

Radius = 2 cm

To find: surface area of cylinder

The volume of cylinder is given as:

`v = \pi r^2 h`

Where "r" is the radius of cylinder and "h" is the height of cylinder

Substituting v = 16π and r = 2 in above formula,

`16 \pi = \pi (2)^2 * h\\\\16 = 4h\\\\h = 4`

Thus height of cylinder is 4 cm

The surface area of cylinder is given as:

`S.A = 2 \pi r^2 + 2 \pi r h`

Substituting h = 4 and r = 2 in above formula,

`S.A = 2 \pi (2)^2 + 2 \pi (2)(4)\\\\S.A = 2 \pi (4) + 2 \pi (8)\\\\S.A = 2 \pi (4 + 8)\\\\S.A = 2 \PI (12)\\\\S.A = 24 \PI`

Thus surface area of cylinder is 24π square centimeter