Chapter 12, Problem 9PT

To determine

To determine the surface area and volume of the Earth.

Answer to Problem 9PT

  $16384\pi \times {10}^4$ kilometer², $349525.33\pi \times {10}^6$ kilometer³

Explanation of Solution

Given:

  

Radius of the Earth $=6400$ kilometer

Formula used:

Surface area of a sphere $=4\pi r^2$

Volume of a sphere, $V=\frac{4}{3}\pi r^3$

Calculation:

For the earth,

Surface area of the Earth $=4\pi r^2$

  $\begin{array}{l}=4\times \pi \times {\left(6400\right)}^2\\ =4\pi \times 4096\times {10}^4\\ =16384\pi \times {10}^4\end{array}$

Volume of the Earth, $V=\frac{4}{3}\pi r^3$

  $\begin{array}{l}=\frac{4}{3}\times \pi \times {\left(6400\right)}^3\\ =\frac{4}{3}\times \pi \times 262144\times {10}^6\\ =349525.33\pi \times {10}^6\end{array}$

Conclusion:

Therefore, surface area of the Earth is $16384\pi \times {10}^4$ kilometer² and volume of the Earth is $349525.33\pi \times {10}^6$ kilometer³.