Question

Find the volume of a sphere with surface area equal to 100pi ft². Use 3.14 for pi and round to the nearest hundredth.

Answer 1

Solve the following, the area of a sphere, for r.\[4\pi r^2=100\]\[r=\frac{5}{\sqrt{\pi }} \]Plug the value of r into the expression for the volume of a sphere and evaluate the result.\[\frac{4}{3}\pi r^3=\frac{4}{3}\pi \left(\frac{5}{\sqrt{\pi }}\right)^3=\frac{500}{3 \sqrt{\pi }}=\text{Round}\left[\frac{500}{3 \sqrt{\pi }},0.01\right]=94.03 \text{ft}^3 \]