Question

what is the volume of this cone? round your answer to the nearest hundredth. 19 m 16 m cubic meters

Explanation:

Step1: Find the radius using Pythagorean theorem

Let the height of the cone be $h$, the slant - height be $l$, and the radius be $r$. We know that $l = 19$ m and $h=16$ m. By the Pythagorean theorem $r=\sqrt{l^{2}-h^{2}}$. So, $r = \sqrt{19^{2}-16^{2}}=\sqrt{(19 + 16)(19 - 16)}=\sqrt{35\times3}=\sqrt{105}\approx10.25$ m.

Step2: Calculate the volume of the cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r\approx10.25$ m and $h = 16$ m into the formula. $V=\frac{1}{3}\pi\times(10.25)^{2}\times16=\frac{1}{3}\pi\times105.0625\times16=\frac{1681\pi}{3}\approx1759.29$ m³.

Answer:

$1759.29$