Question

what is the volume of a sphere with a radius of 36.6 cm, rounded to the nearest tenth of a cubic centimeter?

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the given radius into the formula

Given \( r = 36.6\space cm \), substitute \( r \) into the formula:
\( V=\frac{4}{3}\pi(36.6)^{3} \)
First, calculate \( (36.6)^{3}=36.6\times36.6\times36.6 = 36.6\times1339.56=49027.896 \)
Then, \( \frac{4}{3}\times49027.896=\frac{196111.584}{3} = 65370.528 \)
Now, multiply by \( \pi \) (using \( \pi\approx3.14159 \)):
\( V = 65370.528\times3.14159\approx205379.7 \)

Answer:

\( 205379.7 \)