Chapter 1, Problem 23P

a.

To determine

Surface area of Moon.

Answer to Problem 23P

Surface area of Moon is $3.80\times {10}^7{\text{ km}}^2$

Explanation of Solution

Given :

Diameter of Moon is, $d=3480\text{ km}$

Formula used :

Surface area is,

  $A=4\pi r^2$

Where, r is radius.

Calculation:

Diameter is given by,

  $\begin{array}{l}d=2r\\ 3480=2r\\ r=1740\text{ km}\end{array}$

Now, substituting the value of r and solve.

  $\begin{array}{l}{A}_{moon}=4\times 3.14\times {\left(1740\right)}^2\\ =3.80\times {10}^7{\text{ km}}^2\end{array}$

Conclusion :

Therefore, surface area of Moon is $3.80\times {10}^7{\text{ km}}^2$

b.

To determine

To compare: The surface area of Earth with Moon.

Answer to Problem 23P

Surface area of Earth is 13.421 times of surface area of Moon

Explanation of Solution

Given :

Diameter of Moon is, $d=3480\text{ km}$

Formula used :

Surface area is,

  $A=4\pi r^2$

Where, r is radius.

Calculation:

From part (a), surface area of Moon is,

  $A_{moon}=3.80\times {10}^7{\text{ km}}^2\left(1\right)$

Radius of Earth is , $r=6371\text{ km}$

Now, substituting the value of r and solve.

  $\begin{array}{c}{A}_{earth}=4\times 3.14\times {6371}^2\\ =5.1\times {10}^8{\text{ km}}^2\left(\text{2}\right)\end{array}$

Now, divide equation (2) by equation (1).

  $\begin{array}{l}\frac{A_{earth}}{A_{moon}}=\frac{5.1\times {10}^8}{3.8\times {10}^7}\\ \frac{A_{earth}}{A_{moon}}=13.421\\ A_{earth}=13.421A_{moon}\end{array}$

Conclusion :

Therefore, surface area of Earth is 13.421 times of surface area of Moon.