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 sandpile is 31 feet. Find the volume of the pile of sand.

Correct answer:

V =  3179.8926 ft³

Step-by-step explanation:

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

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