Question

what is the volume of this cone? round your answer to the nearest hundredth. 18 m 11 m cubic meters submit

Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$, where $r$ is the radius and $h$ is the height. Here $r = 11$ m and we need to find the height using the Pythagorean - theorem in the cone. The slant - height $l = 18$ m. Let the height be $h$. Then $h=\sqrt{l^{2}-r^{2}}$.

Step2: Calculate the height

$h=\sqrt{18^{2}-11^{2}}=\sqrt{(18 + 11)(18 - 11)}=\sqrt{29\times7}=\sqrt{203}\approx14.25$ m.

Step3: Calculate the volume

$V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times\pi\times11^{2}\times14.25=\frac{1}{3}\times\pi\times121\times14.25=\frac{1724.25\pi}{3}\approx1805.69$ $m^{3}$.

Answer:

$1805.69$