Question

question 3 of 10
the formula for the volume of a sphere is v = ⅓πr³, where v is the volume and r is the radius. solve the formula for r, and then use it to answer the question
the volume of a soccer ball is about 371 cubic inches.
what is the radius of the soccer ball, to the nearest tenth of an inch? use 3.14 for π.
a. 4.5 inches
b. 4.1 inches
c. 4.7 inches
d. 4.3 inches

Explanation:

Step1: Solve the volume formula for r

Given $V = \frac{4}{3}\pi r^{3}$, first, isolate $r^{3}$:
$r^{3}=\frac{3V}{4\pi}$
Then, take the cube - root of both sides:
$r=\sqrt[3]{\frac{3V}{4\pi}}$

Step2: Substitute the given values

We know that $V = 371$ cubic inches and $\pi=3.14$.
$r=\sqrt[3]{\frac{3\times371}{4\times3.14}}$
$r=\sqrt[3]{\frac{1113}{12.56}}$
$r=\sqrt[3]{88.6147}$
$r\approx4.45\approx4.5$ inches

Answer:

A. 4.5 inches