Question

a toy in the shape of a sphere expands and contracts. when it is completely closed, it has a diameter of 17.5 inches. find the volume of the sphere when it is completely closed. (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 $square$ cu in. (round to the nearest whole number as needed.)

Explanation:

Step1: Find the radius

The diameter $d = 17.5$ inches. The radius $r=\frac{d}{2}=\frac{17.5}{2}=8.75$ inches.

Step2: Use the volume formula

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. Substitute $r = 8.75$ and $\pi=3.14$ into the formula.
$V=\frac{4}{3}\times3.14\times(8.75)^{3}$
$V=\frac{4}{3}\times3.14\times669.921875$
$V=\frac{4\times3.14\times669.921875}{3}$
$V=\frac{8414.80625}{3}$
$V = 2804.935417$

Step3: Round to the nearest whole number

Rounding $2804.935417$ to the nearest whole number gives $2805$.

Answer:

$2805$ cu in