Volcano

The crater of a volcano is approximately in the shape of a cone of a base 3.1416 square miles. The crater's depth is 1500 ft. How many cubic yards of earth would be required to fill this cavity?

Correct answer:

x =  1621903360 yd³

Step-by-step explanation:

$$\begin{gathered} S_1=3.1416{\text{mi}}^2 \\ S=S_1\cdot 3097600=3.1416\cdot 3097600=9731420.16{\text{yd}}^2 \\ h=1500\text{ft}\to \text{yd}=1500:3\text{yd}=500\text{yd} \\ x=\frac{1}{3}\cdot S\cdot h=\frac{1}{3}\cdot 9731420.16\cdot 500=1621903360{\text{yd}}^3=1.622\cdot 10^9{\text{yd}}^3 \end{gathered}$$

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