Question

a toy ball in the shape of a sphere expands and contracts. when it is completely closed, it has a diameter of 7.5 inches. find the volume of the sphere when it is completely closed. (hint: the volume of a sphere of radius r is $\frac{4}{3}pi r^{3}$. ) use 3.14 for $pi$. the volume of the sphere is approximately $square$ (round to the nearest whole number as needed.)

Explanation:

Step1: Find the radius

The diameter $d = 7.5$ inches. The radius $r=\frac{d}{2}=\frac{7.5}{2}=3.75$ inches.

Step2: Use the volume - formula for a sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. Substitute $r = 3.75$ and $\pi=3.14$ into the formula.
$V=\frac{4}{3}\times3.14\times(3.75)^{3}$
$V=\frac{4}{3}\times3.14\times52.734375$
$V = 4\times3.14\times17.578125$
$V=219.91125$

Step3: Round to the nearest whole number

Rounding $219.91125$ to the nearest whole number gives $220$.

Answer:

$220$