Question

find the volume of the cone. either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth. units³

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 of the cone.

Step2: Identify the values of \( r \) and \( h \)

From the diagram, the radius \( r = 3 \) and the height \( h=4 \).

Step3: Substitute the values into the formula

Substitute \( r = 3 \) and \( h = 4 \) into the formula \( V=\frac{1}{3}\pi r^{2}h \). We get \( V=\frac{1}{3}\times\pi\times3^{2}\times4 \).
First, calculate \( 3^{2}=9 \). Then the expression becomes \( V=\frac{1}{3}\times\pi\times9\times4 \).
\( \frac{1}{3}\times9 = 3 \), so \( V = 3\times\pi\times4=12\pi \).
If we use \( \pi = 3.14 \), then \( V=12\times3.14 = 37.68 \).

Answer:

\( 12\pi \) (or \( 37.68 \))