Pile of sand

A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.

Correct result:

V =  3179.893 ft³

Solution:

$s=20 \ \text{ft} \ \\ D=31 \ \text{ft} \ \\ \ \\ r=D/2=31/2=\dfrac{ 31 }{ 2 }=15.5 \ \text{ft} \ \\ \ \\ S=\pi \cdot \ r^2=3.1416 \cdot \ 15.5^2 \doteq 754.7676 \ \text{ft}^2 \ \\ \ \\ s^2=h^2 + r^2 \ \\ \ \\ h=\sqrt{ s^2-r^2 }=\sqrt{ 20^2-15.5^2 } \doteq 12.6392 \ \text{ft} \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 754.7676 \cdot \ 12.6392=3179.893 \ \text{ft}^3$

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