Question

what is the volume of this cone? round your answer to the nearest hundredth. 37 yd 31 yd cubic yards

Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$. Here, the radius $r = 31$ yd and the height $h=37$ yd.

Step2: Substitute values

$V=\frac{1}{3}\times\pi\times(31)^{2}\times37$. First, calculate $(31)^{2}=31\times31 = 961$. Then, $V=\frac{1}{3}\times\pi\times961\times37$.
$961\times37 = 35557$. So, $V=\frac{35557\pi}{3}$.

Step3: Calculate and round

$V=\frac{35557\pi}{3}\approx\frac{35557\times3.14159}{3}\approx\frac{111771.47463}{3}\approx37257.16$ cubic yards.

Answer:

$37257.16$