Question

find the volume of a cone with a height of 10 cm and a base diameter of 12 cm. 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: Find the radius of the base

The diameter $d = 12$ cm, and the radius $r=\frac{d}{2}=\frac{12}{2}=6$ cm.

Step2: Use the volume formula for a cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 6$ cm, $h = 10$ cm and $\pi=3.14$ into the formula. So $V=\frac{1}{3}\times3.14\times6^{2}\times10$.

Step3: Calculate the volume

First, $6^{2}=36$. Then $\frac{1}{3}\times3.14\times36\times10=( \frac{1}{3}\times36)\times3.14\times10 = 12\times3.14\times10=376.8$ $cm^{3}$.

Answer:

$376.8$ $cm^{3}$