Question

question 3 of 10. the formula for the volume of a sphere is v = 4/3πr³, 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 π. a. 4.5 inches b. 4.1 inches c. 4.3 inches d. 4.7 inches

Explanation:

Step1: Isolate $r^{3}$

Starting with $V=\frac{4}{3}\pi r^{3}$, we first 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 $\pi=3.14$

$r=\sqrt[3]{\frac{3\times435}{4\times3.14}}=\sqrt[3]{\frac{1305}{12.56}}\approx\sqrt[3]{103.9}$.
Using a calculator, $\sqrt[3]{103.9}\approx4.7$.

Answer:

D. 4.7 inches