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:

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

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