Volcano

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

Correct result:

x =  1621903360 yd³

Solution:

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

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Showing 1 comment:

Math student

Why did you multiply the base by 3097600 and why did you divide the height by 3 .

9 months ago  2 Likes Like

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