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 $1022.65 \ in^3$

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

$r=\frac{d}{2}$

$r=\frac{12.5}{2}$

$r=6.25 \ in$

Thus, the radius of the toy ball is 6.25 in

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

$V=\frac{4}{3} \pi r^{3}$

Substituting the values, we get,

$V=\frac{4}{3} \pi(6.25)^{3}$

Multiplying, we get,

$V=\frac{976.5625 \pi}{3}$

Substituting $\pi=3.14$, we have,

$V=\frac{976.5625 (3.14)}{3}$

Simplifying, we get,

$V=1022.65 \ in^3$

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