Chapter 2.1, Problem 49PS

Solution

To find: The volume of each ocean

The volumes of the four oceans are $6.2858\times {10}^{17}$ cubic meters, $3.01824\times {10}^{17}$ cubic meters, $2.71656\times {10}^{17}$ cubic meters, and $1.7061\times {10}^{16}$ cubic meters.

Given information:

The table shows the surface areas and average depths of four oceans.

  

Calculation:

Consider the following table.

  

From the given table, it can be seen that the surface area of the first ocean is $1.56\times {10}^{14}$ square meters, and its average depth is $4.03\times {10}^3$ meters.

The volume of the ocean is given by the product of its surface area and average depth.

Volume $=$ Surface area $\times$ Average depth

  $=\left(1.56\times {10}^{14}\right)\left(4.03\times {10}^3\right)$

Apply the properties of multiplication to rearrange the terms.

  $\begin{array}{c}\left(1.56\times {10}^{14}\right)\left(4.03\times {10}^3\right)=\left(1.56\times 4.03\right)\left({10}^{14}\times {10}^3\right)\\ =6.2868\left({10}^{14}\times {10}^3\right)\end{array}$

Now, simplify using a property of exponents $a^m\cdot a^n=a^{m+n}$ .

  $\begin{array}{c}6.2868\left({10}^{14}\times {10}^3\right)=6.2858\times {10}^{14+3}\\ =6.2858\times {10}^{17}\end{array}$

Therefore, the volume of the first ocean is $6.2858\times {10}^{17}$ cubic meters.

In a similar way, calculate the volumes of the other three oceans.

  $\begin{array}{c}\text{Volume of the second ocean }=\left(7.68\times {10}^{13}\right)\left(3.93\times {10}^3\right)\\ =30.1824\times {10}^{16}\\ =3.01824\times {10}^{17}\end{array}$

Now, find the volume of the third ocean.

  $\begin{array}{c}\text{Volume of the third ocean}=\left(6.86\times {10}^{13}\right)\left(3.96\times {10}^3\right)\\ =27.1656\times {10}^{16}\\ =2.71656\times {10}^{17}\end{array}$

Next, find the volume of the fourth ocean.

  $\begin{array}{c}\text{Volume}\text{of}\text{the}\text{fourth}\text{ocean}=\left(1.41\times {10}^{13}\right)\left(1.21\times {10}^3\right)\\ =1.7061\times {10}^{16}\end{array}$

Therefore, the volumes of the four oceans are $6.2858\times {10}^{17}$ cubic meters, $3.01824\times {10}^{17}$ cubic meters, $2.71656\times {10}^{17}$ cubic meters, and $1.7061\times {10}^{16}$ cubic meters.