Question

A plane intersects the center of a sphere with the volume of about 9202.8 m. What is the area of the cross section?

Answer 1

First, let's use the formula for the volume of a sphere to find its radius:

$\begin{gathered} V=\frac{4}{3}\pi r^3\\ \\ 9202.8=\frac{4}{3}\cdot3.1416\cdot r^3\\ \\ r^3=\frac{9202.8}{\frac{4}{3}\cdot3.1416}\\ \\ r^3=2197\\ \\ r=13\text{ m} \end{gathered}$

Now, to calculate the area, let's use the formula for the area of a circle:

$\begin{gathered} A=\pi r^2\\ \\ A=3.1416\cdot13^2\\ \\ A=530.9\text{ m^^b2} \end{gathered}$