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 3877 (round to the nearest whole number as needed.) sq in. cu in. in.

Explanation:

Step1: Calculate the radius

The radius $r$ is half of the diameter. Given diameter $d = 19.5$ inches, so $r=\frac{d}{2}=\frac{19.5}{2}=9.75$ inches.

Step2: Use the volume formula

The volume formula of a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = 9.75$ inches and $\pi=3.14$ into the formula:
$V=\frac{4}{3}\times3.14\times(9.75)^{3}$
$V=\frac{4}{3}\times3.14\times923.4953125$
$V = 4\times3.14\times307.8317708$
$V=3877.297508$

Step3: Round to the nearest whole number

Rounding $3877.297508$ to the nearest whole number gives $3877$.

Answer:

$3877$ cu in.