Question

what is the volume of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 19 cm 12 cm cubic centimeters

Explanation:

Step1: Recall volume formula for cone

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, the radius $r = 12$ cm and we need to find the height. Using the Pythagorean theorem for the right - triangle formed by the slant height $l = 19$ cm, radius $r = 12$ cm and height $h$. We know that $l^{2}=h^{2}+r^{2}$, so $h=\sqrt{l^{2}-r^{2}}=\sqrt{19^{2}-12^{2}}=\sqrt{(19 + 12)(19 - 12)}=\sqrt{31\times7}=\sqrt{217}\approx14.73$ cm.

Step2: Calculate volume

Substitute $r = 12$ cm and $h\approx14.73$ cm and $\pi\approx3.14$ into the volume formula $V=\frac{1}{3}\pi r^{2}h$.
$V=\frac{1}{3}\times3.14\times12^{2}\times14.73$
$V=\frac{1}{3}\times3.14\times144\times14.73$
$V = 3.14\times48\times14.73$
$V=3.14\times707.04$
$V\approx2220.10$ cm³

Answer:

$2220.10$