Chapter 10.2, Problem 16Q

To determine

To graph the function and find volume of Spaceship Earth.

Answer to Problem 16Q

Volume $V=65476.19m^3$

Explanation of Solution

Given information: $r=\sqrt[3]{\frac{3}{4\pi }V}$ , Radius r = 25 meters, Volume V

Formula Used:Volume of Sphere.

Calculation:

  $r=\sqrt[3]{\frac{3}{4\pi }V}$

Now, cubing both sides.

  $r^3=\frac{3}{4\pi }V$

So,

  $V=\frac{4\pi r^3}{3}$

Graph of $V=\frac{4\pi r^3}{3}$

  $\begin{array}{cccc}r& 0& \frac{1}{2}& 1\\ V& 0& \frac{\pi }{6}& \frac{4\pi }{3}\end{array}$

  

Radius r = 25 meters.

Volume $V=\frac{4\pi r^3}{3}$

So, Put value of radius r to find volume

  $V=\frac{4\pi {\left(25\right)}^3}{3}{m}^3$

So,

  $V=\frac{4}{3}\times \frac{22}{7}\times 25\times 25\times 25m^3$

Now,

  $V=\frac{1375000}{21}{m}^3$

Hence,

Volume $V=65476.19m^3$