A cylinder has a radius of 6 inches and height of 3 and 3/4 inches. A sphere has a radius of 6 inches. What is the difference between the volume, to the nearest tenth of a cubic inch of the cylinder and sphere

Difference = 480.9 in³

Step-by-step explanation:

Given

Cylinder;

Height, h = 3¾ inches

Radius, r₁ = 6 inches

Sphere

Radius, r₂ = 6 inches

The volume of a cylinder is calculated as thus

Volume, V₁ = πr₁²h

The volume of a sphere is calculated as this

Volume, V₂ = 4/3 πr₂³

Calculating the volume of the cylinder

V₁ = πr₁²h becomes

V₁ = π * 6² * 3¾

V₁ = π * 36 * 3¾

V₁ = π * 36 * 15/4

V₁ = π * 540/4

V₁ = π * 135

V₁ = 135π in³

Calculating the volume of the sphere

V₂ = 4/3 πr₂³ becomes

V₂ = 4/3 * π * 6³

V₂ = 4/3 * π * 216

V₂ = 864/3 * π

V₂ = 288π in³

The difference between the volume is calculated as thus.

Difference = V₂ - V₁

Difference = 288π - 135π

Difference = 153π

Take π as 22/7

Difference = 153 * 22/7

Difference = 480.9 in³ (Approximated)