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 ft D=31 ft  r=D/2=31/2=312=15.5 ft  S=π r2=3.1416 15.52754.7676 ft2  s2=h2+r2  h=s2r2=20215.5212.6392 ft  V=13 S h=13 754.7676 12.6392=3179.893 ft3s=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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