Question

what is the volume of this cone? round your answer to the nearest hundredth. cubic feet

Explanation:

Step1: Find the radius

Use the Pythagorean theorem in the cone - cross - section. The slant height $l = 13$ ft and height $h=12$ ft. Let the radius be $r$. By $l^{2}=h^{2}+r^{2}$, we have $r=\sqrt{l^{2}-h^{2}}$.
$r = \sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5$ ft.

Step2: Calculate the volume

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 5$ ft and $h = 12$ ft into the formula.
$V=\frac{1}{3}\pi\times5^{2}\times12=\frac{1}{3}\pi\times25\times12 = 100\pi$ cubic feet.

Step3: Round the result

$V\approx100\times3.14159 = 314.16$ cubic feet.

Answer:

$314.16$