Question

what is the volume of a sphere with a radius of 24.2 ft, rounded to the nearest tenth of a cubic foot?

Explanation:

Step1: Recall volume formula

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$, where $r$ is the radius.

Step2: Substitute the radius value

Given $r = 24.2$ ft, we substitute it into the formula: $V=\frac{4}{3}\pi(24.2)^{3}$.
First, calculate $(24.2)^{3}=24.2\times24.2\times24.2 = 14172.488$.
Then, $V=\frac{4}{3}\pi\times14172.488$.
$\frac{4}{3}\times14172.488 = 18896.65067$.
So, $V = 18896.65067\pi$.

Step3: Calculate the value

Using $\pi\approx3.14159$, we have $V\approx18896.65067\times3.14159$.
$V\approx59387.9$.

Answer:

$59387.9$ cubic - feet