Chapter 12.4, Problem 6CE

To determine

To complete: Copy and complete the table for sphere.

Answer to Problem 6CE

Radius will be 10 and area is $400\pi$ .

Explanation of Solution

Given information:

The given volume is $\frac{4000\pi }{3}$ .

Calculation:

The Area of sphere is given by

  $A=4\pi r^2$ and

The Volume is given by

  $V=\frac{4}{3}\pi r^3$ .

Here volume $V=\frac{4000\pi }{3}$ . Therefore,

  $\begin{array}{l}\frac{4}{3}\pi r^3=\frac{4000\pi }{3}\\ r^3=\frac{4000\pi }{3}\times \frac{3}{4\pi }\\ r^3=\frac{4000\cancel{\pi }}{\cancel{3}}\times \frac{\cancel{3}}{4\cancel{\pi }}\\ r^3=1000\\ r=10\end{array}$

Now, Area

  $\begin{array}{l}A=4\pi {\left(10\right)}^2\\ A=4\pi \times 100\\ A=400\pi \end{array}$

Hence,

Radius will be 10 and area is $400\pi$ .