Question

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

Explanation:

Step1: Write the formula for the volume of a cone

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

Step2: Substitute the given values into the formula

Given \( r = 11 \) inches and \( h=11 \) inches. Substitute into the formula: \( V=\frac{1}{3}\pi\times(11)^{2}\times11 \).
First, calculate \( (11)^{2}\times11=11^{3}=1331 \). Then \( V=\frac{1331}{3}\pi \).

Step3: Calculate the numerical value

\( \pi\approx3.14159 \), so \( V=\frac{1331}{3}\times3.14159 \).
\( \frac{1331}{3}\approx443.6667 \), and \( 443.6667\times3.14159\approx1393.94 \).

Answer:

\( 1393.94 \)