Question

a cone has a height of 11 inches and a diameter of 16 inches. what is its volume? round your answer to the nearest hundredth. cubic inches submit

Explanation:

Step1: Find the radius of the cone

The diameter is 16 inches, so the radius \( r=\frac{16}{2} = 8 \) inches.

Step2: Recall the formula for the volume of a cone

The volume \( V \) of a cone is given by \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know \( r = 8 \) inches and \( h=11 \) inches. So,
\[

$$\begin{align*} V&=\frac{1}{3}\times\pi\times(8)^{2}\times11\\ &=\frac{1}{3}\times\pi\times64\times11\\ &=\frac{704\pi}{3}\\ &\approx\frac{704\times3.14159}{3}\\ &\approx\frac{2210.58}{3}\\ &\approx736.86 \end{align*}$$

\]

Answer:

\( 736.86 \)