Question

find the volume of a cone with a height of 9 m and a base radius of 5 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 volume formula for a cone

The volume formula for 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 \( r = 5\space m \), \( h=9\space m \), and \( \pi = 3.14 \).
Substitute into the formula: \( V=\frac{1}{3}\times3.14\times5^{2}\times9 \).
First calculate \( 5^{2}=25 \).
Then \( V=\frac{1}{3}\times3.14\times25\times9 \).
Since \( \frac{1}{3}\times9 = 3 \), the formula simplifies to \( V=3.14\times25\times3 \).
Calculate \( 25\times3 = 75 \).
Then \( V=3.14\times75 \).

Step3: Calculate the final value

\( 3.14\times75=235.5 \).

Answer:

\( 235.5\space m^{3} \)