Question

a cone has a height of 4 feet and a radius of 3 feet. what is its volume? round your answer to the nearest hundredth. blank cubic feet submit

Explanation:

Step1: Recall the formula for the volume of a cone

The volume \( V \) of a cone is given by the formula \( V = \frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute the given values into the formula

We are given that \( r = 3 \) feet and \( h = 4 \) feet. Substituting these values into the formula, we get:
\( V=\frac{1}{3}\times\pi\times(3)^{2}\times4 \)
First, calculate \( (3)^{2}=9 \). Then the expression becomes:
\( V=\frac{1}{3}\times\pi\times9\times4 \)
Simplify \( \frac{1}{3}\times9 = 3 \), so now we have:
\( V = 3\times\pi\times4 \)
\( V = 12\pi \)

Step3: Calculate the numerical value and round

Using \( \pi\approx3.14159 \), we have \( V = 12\times3.14159 = 37.69908 \). Rounding to the nearest hundredth, we look at the thousandth place, which is 9. Since \( 9\geq5 \), we round up the hundredth place. So \( 37.69908\approx37.70 \).

Answer:

\( 37.70 \)