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:

S=3.1416⋅ 3097600=9731420.16 yd2 h=1500 ft→yd=1500/3 yd=500 yd  x=13⋅ S⋅ h=13⋅ 9731420.16⋅ 500=1621903360 yd3=1.621903⋅109 yd3S=3.1416 \cdot \ 3097600=9731420.16 \ \text{yd}^2 \ \\ h=1500 \ ft \rightarrow yd=1500 / 3 \ yd=500 \ yd \ \\ \ \\ x=\dfrac{ 1 }{ 3 } \cdot \ S \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 9731420.16 \cdot \ 500=1621903360 \ \text{yd}^3=1.621903\cdot 10^{ 9 } \ \text{yd}^3

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

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