Question

find the volume of a cone with a base radius of 4 m and a height of 12 m. 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 and \( h \) is the height.

Step2: Substitute the given values into the formula

Given \( r = 4\space m \), \( h=12\space m \), and \( \pi = 3.14 \).
Substitute these values into the formula:
\( V=\frac{1}{3}\times3.14\times4^{2}\times12 \)
First, calculate \( 4^{2}=16 \).
Then the expression becomes \( V=\frac{1}{3}\times3.14\times16\times12 \)
Since \( \frac{1}{3}\times12 = 4 \), the formula simplifies to \( V=3.14\times16\times4 \)
\( 16\times4=64 \), so \( V = 3.14\times64 \)
\( 3.14\times64=(3 + 0.14)\times64=3\times64+0.14\times64=192+8.96 = 200.96 \)

Answer:

\( 200.96\space m^{3} \)