Question

a toy ball in the shape of a sphere expands and contracts. when it is completely closed, it has a diameter of 19.5 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 $\frac{4}{3}pi r^{3}$.) the volume of the sphere is approximately (round to the nearest whole number as needed.)

Explanation:

Step1: Find the radius

The diameter $d = 19.5$ inches. The radius $r=\frac{d}{2}$. So $r=\frac{19.5}{2}=9.75$ inches.

Step2: Calculate the volume

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. Substitute $r = 9.75$ and $\pi=3.14$ into the formula.
$V=\frac{4}{3}\times3.14\times(9.75)^{3}$.
First, calculate $(9.75)^{3}=9.75\times9.75\times9.75 = 926.40625$.
Then, $\frac{4}{3}\times3.14\times926.40625=\frac{4\times3.14\times926.40625}{3}$.
$4\times3.14\times926.40625 = 11631.99$.
$\frac{11631.99}{3}=3877.33$.
Rounding to the nearest whole - number, $V\approx3877$ cubic inches.

Answer:

3877