Question

what is the volume of this cone? round your answer to the nearest hundredth. 19 cm 16 cm cubic centimeters submit

Explanation:

Step1: Find the height of the cone

Use the Pythagorean theorem \(h = \sqrt{l^{2}-r^{2}}\), where \(l = 19\) (slant height) and \(r = 16\) (radius).
\(h=\sqrt{19^{2}-16^{2}}=\sqrt{(19 + 16)(19 - 16)}=\sqrt{35\times3}=\sqrt{105}\approx10.25\)

Step2: Calculate the volume of the cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\).
Substitute \(r = 16\) and \(h\approx10.25\) into the formula:
\(V=\frac{1}{3}\times\pi\times16^{2}\times10.25=\frac{1}{3}\times\pi\times256\times10.25=\frac{2624}{3}\pi\approx\frac{2624}{3}\times3.14\)
\(V\approx2749.71\)

Answer:

\(2749.71\)