Question

find the volume of a cone with a height of 11 in and a base radius of 6 in. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit in your answer.

Explanation:

Step1: Recall 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 of the base and \( h \) is the height.

Step2: Substitute the given values into the formula

Given \( r = 6\) in, \( h=11\) in, and \( \pi = 3.14\).
Substitute these values: \( V=\frac{1}{3}\times3.14\times6^{2}\times11\).
First, calculate \( 6^{2}=36\).
Then the expression becomes \( V=\frac{1}{3}\times3.14\times36\times11\).
Since \( \frac{1}{3}\times36 = 12\), the expression simplifies to \( V=3.14\times12\times11\).
Next, \( 12\times11 = 132\).
So \( V=3.14\times132\).

Step3: Calculate the final value

\( 3.14\times132=(3 + 0.14)\times132=3\times132+0.14\times132=396+18.48 = 414.48\).

Answer:

\( 414.48\) cubic inches.