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. 4.7 inches
b. 4.3 inches
c. 4.5 inches
d. 4.1 inches

Explanation:

Step1: Isolate $r^3$ term

Multiply both sides by $\frac{3}{4\pi}$:
$$r^3 = \frac{3V}{4\pi}$$

Step2: Substitute given values

Plug $V=435$, $\pi=3.14$:
$$r^3 = \frac{3\times435}{4\times3.14} = \frac{1305}{12.56} \approx 103.90$$

Step3: Solve for $r$

Take cube root of the result:
$$r = \sqrt[3]{103.90} \approx 4.7$$

Answer:

A. 4.7 inches