Question

A toy ball in the shape of a sphere expands and contracts. When it is completely​ closed, it has a diameter of 12.5 inches.Find the volume of the sphere when it is completely closed. Use 3.14 for

π.
(Hint: the volume of a sphere of radius r is
4/3πr3.
​

Answer 1

The volume of the sphere is
`1022.65 \ in^3`

Step-by-step explanation:

Given that the diameter of the toy ball is 12.5 inches

We need to determine the volume of the toy ball.

The radius of the toy ball is given by

`r=(d)/(2)`

`r=(12.5)/(2)`

`r=6.25 \ in`

Thus, the radius of the toy ball is 6.25 in

The volume of the sphere can be determined using the formula,

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

Substituting the values, we get,

`V=(4)/(3) \pi(6.25)^(3)`

Multiplying, we get,

`V=(976.5625 \pi)/(3)`

Substituting
`\pi=3.14`, we have,

`V=(976.5625 (3.14))/(3)`

Simplifying, we get,

`V=1022.65 \ in^3`

Thus, the volume of the sphere is
`1022.65 \ in^3`