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 the formula for the volume of a sphere

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

Step2: Substitute the given radius into the formula

Given that the radius \( r = 24.2\space\text{ft} \), we substitute this value into the formula:
\( V=\frac{4}{3}\pi(24.2)^{3} \)
First, calculate \( (24.2)^{3} \):
\( 24.2\times24.2\times24.2 = 24.2\times585.64=14172.488 \)
Then, multiply by \( \frac{4}{3}\pi \):
\( V=\frac{4}{3}\pi\times14172.488 \)
\( V=\frac{56689.952}{3}\pi \)
\( V\approx18896.6507\times\pi \)
Using \( \pi\approx3.14159 \), we get:
\( V\approx18896.6507\times3.14159 \)
\( V\approx59365.9 \) (rounded to the nearest tenth)

Answer:

The volume of the sphere is approximately \( 59365.9 \) cubic feet.