Question

A cylinder has a radius of 3 inches and a height of 4 inches. a sphere has a radius of 2 inches. what is the difference between the volume, to the nearest tenth of a cubic inch, of the cylinder and the sphere?

A. 29.3

B. 79.6

C. 146.6

D. 305.8

Answer 1

Option B

Difference between volume of cylinder and sphere is 79.51

Solution:

Given that,

Cylinder has a radius of 3 inches and a height of 4 inches

Volume of cylinder is given as:

`V = \pi r^2 h`

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

r = 3 inches

h = 4 inches

Substituting the value, we get

`V = 3.14 * 3^2 * 4\\\\V = 3.14 * 9 * 4 = 3.14 * 36\\\\V = 113.04 \approx 113`

Thus volume of cylinder is 113 cubic inches

A sphere has a radius of 2 inches

Volume of sphere is given as:

`V = (4)/(3) * \pi * r^3`

Here, r = radius = 2 inches

Substituting the value, we get

`V = (4)/(3) * 3.14 * 2^3\\\\V = (4)/(3) * 3.14 * 8\\\\V = (4)/(3) * 25.12\\\\V = 33.49`

Thus volume of sphere is 33.49 cubic inches

Difference between volume of cylinder and sphere

Difference = volume of cylinder - volume of sphere

Difference = 113 - 33.49 = 79.51

Thus Option B is correct