Question

the diameter of a basketball is 9.50 inches. what is the volume of the ball, rounded to the nearest hundredth?
a. 359.14 in³
b. 437.48 in³
c. 448.92 in³
d. 596.90 in³

Explanation:

Step1: Find the radius

The radius $r$ of a sphere is half of the diameter $d$. Given $d = 9.50$ inches, so $r=\frac{d}{2}=\frac{9.50}{2}=4.75$ inches.

Step2: Use the volume formula for a sphere

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = 4.75$ into the formula: $V=\frac{4}{3}\pi(4.75)^{3}$.
$V=\frac{4}{3}\pi\times107.171875\approx\frac{4}{3}\times3.14159\times107.171875$.
$V=\frac{4\times3.14159\times107.171875}{3}\approx448.92$ $in^{3}$.

Answer:

C. $448.92$ $in^{3}$