Question

question 7 of 10
the formula for the volume of a sphere is $v=\frac{4}{3}pi r^{3}$, 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 basketball is about 435 cubic inches.
what is the radius of the basketball, to the nearest tenth of an inch? use 3.14 for $pi$
a. 4.3 inches
b. 4.5 inches
c. 4.1 inches
d. 4.7 inches

Explanation:

Step1: Isolate $r^{3}$

Starting with $V=\frac{4}{3}\pi r^{3}$, multiply both sides by $\frac{3}{4\pi}$ to get $r^{3}=\frac{3V}{4\pi}$.

Step2: Solve for $r$

Take the cube - root of both sides: $r = \sqrt[3]{\frac{3V}{4\pi}}$.

Step3: Substitute $V = 435$ and $\pi=3.14$

$r=\sqrt[3]{\frac{3\times435}{4\times3.14}}=\sqrt[3]{\frac{1305}{12.56}}\approx\sqrt[3]{103.90}$.
Calculating $\sqrt[3]{103.90}\approx4.7$.

Answer:

D. 4.7 inches