Question

The volume of a sphere is a radius r is given by the formula V=4/3For the volume of a sphere with diameter 30 inches. Round to two decimals

Answer 1

14,137.17 cubic inches.

Explanation:

The volume of a sphere with a radius, r is given by the formula:

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

We are given that the diameter of the sphere = 30 inches.

First, we have to find the radius of the sphere.

`\text{Radius}=\frac{\text{Diameter}}{2}=(30)/(2)=15\text{ inches}`

Next, substitute r=15 inches into the formula for volume.

`\begin{gathered} V=(4)/(3)*\pi*15^3 \\ =(4)/(3)*\pi*3375 \\ =4500\pi \\ =14137.17\; in.^3 \end{gathered}`

The volume of the sphere is 14,137.17 cubic inches (correct to 2 decimal places).