Chapter 1.2, Problem 97E

Volume of the Oceans The average ocean depth is 3.7 × 10³ m, and the area of the oceans is 3.6 × 10¹⁴ m². What is the total volume of the ocean in liters? (One cubic meter contains 1000 liters.)

To determine

The total volume of the ocean in liters.

Answer to Problem 97E

The total volume of the ocean is $\underset{\_}{1.332\times {10}^{21}\text{liters}}$.

Explanation of Solution

Given that, the average ocean depth is $3.7\times {10}^3\text{m}$ and the area of the ocean is $3.6\times {10}^{14}{\text{m}}^2$.

It is known that, one cubic meter contains 1000 liters.

Substitute $3.6\times {10}^{14}{\text{m}}^2$ for Area of the ocean and $3.7\times {10}^3\text{m}$ for Average Ocean Depth in the formula to calculate volume of the ocean as shown below.

$\begin{array}{c}\text{Volume}\text{of}\text{the}\text{ocean}=3.6\times {10}^{14}{\text{m}}^2\times 3.7\times {10}^3\text{m}\\ =3.6\times {10}^{14}\times 3.7\times {10}^3{\text{m}}^3\\ =3.6\times 3.7\times {10}^{14}\times {10}^3{\text{m}}^3\end{array}$

Use the law of exponents and simplify the above expression,

$\begin{array}{c}\text{Volume of the ocean}=13.32\times {10}^{14+3}{\text{m}}^3\left(a^m\cdot a^n=a^{m+n}\right)\\ =13.32\times {10}^{17}{\text{m}}^3\end{array}$

Now, move decimal 1 place to the left and add 1 to the power of 10 to write the above quantity in proper scientific notation as shown below.

$\begin{array}{c}\text{Volume}\text{of}\text{the}\text{ocean}=13.32\times {10}^{17}{\text{m}}^3\\ =1.332\times {10}^{18}{\text{m}}^3\end{array}$

It is known that, $1{\text{m}}^3=1000\text{liters}$.

Use the above unit conversion of ${\text{m}}^3$ into liters to convert volume of the ocean in ${\text{m}}^3$ into liters as shown below.

$\begin{array}{c}\text{Volume}\text{of}\text{the}\text{ocean}=1.332\times {10}^{18}{\text{m}}^3\\ =1.332\times {10}^{18}\times 1{\text{m}}^3\\ =1.322\times {10}^{18}\times 1000\text{liters}\\ \text{=1}\text{.322}\times {10}^{18}\times {10}^3\text{liters}\end{array}$

Use the law of exponents and further simplify the above expression.

$\begin{array}{c}\text{Volume of the ocean}=\text{1}\text{.322}\times {10}^{18}\times {10}^3\text{liters}\\ =1.332\times {10}^{18+3}\text{liters}\\ =1.332\times {10}^{21}\text{liters}\end{array}$

Therefore, the total volume of the ocean is $\underset{\_}{1.332\times {10}^{21}\text{liters}}$.