A cone

A cone measures 6 inches in diameter at the base. The distance from the edge of the circumference to the top is 12 inches. Find its volume.

Correct answer:

V =  109.506 in³

Step-by-step explanation:

$$\begin{gathered} D=6\text{in} \\ s=12\text{in} \\ r=D/2=6/2=3\text{in} \\ {s}^2=r^2+h^2 \\ h=\sqrt{s^2-r^2}=\sqrt{12^2-3^2}=3\sqrt{15}\text{in}\doteq 11.619\text{in} \\ V=\frac{1}{3}\cdot \pi \cdot r^2\cdot h=\frac{1}{3}\cdot 3.1416\cdot 3^2\cdot 11.619=109.506{\text{in}}^3 \end{gathered}$$

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