Question

what is the volume of this cone? round your answer to the nearest hundredth. 15.1 in 6 in cubic inches

Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Here, the radius $r = 6$ in and we need to find the height $h$. Using the Pythagorean theorem for the cone (slant - height $l = 15.1$ in, $r = 6$ in), $h=\sqrt{l^{2}-r^{2}}$.

Step2: Calculate the height

$h=\sqrt{15.1^{2}-6^{2}}=\sqrt{228.01 - 36}=\sqrt{192.01}\approx13.86$ in.

Step3: Calculate the volume

$V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times\pi\times6^{2}\times13.86=\frac{1}{3}\times\pi\times36\times13.86 = 166.32\pi\approx522.64$ cubic inches.

Answer:

$522.64$