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.

Result

V =  3179.893 ft³

Solution:

$s = 20 \ ft \ \\ D = 31 \ ft \ \\ \ \\ r = D/2 = 31/2 = \dfrac{ 31 }{ 2 } = 15.5 \ ft \ \\ \ \\ S = \pi \cdot \ r^2 = 3.1416 \cdot \ 15.5^2 \doteq 754.7676 \ ft^2 \ \\ \ \\ s^2 = h^2 + r^2 \ \\ \ \\ h = \sqrt{ s^2-r^2 } = \sqrt{ 20^2-15.5^2 } \doteq 12.6392 \ ft \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 754.7676 \cdot \ 12.6392 \doteq 3179.8926 = 3179.893 \ ft^3$

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