Question

a cone has a height of 9 meters and a radius of 3 meters. what is its volume? round your answer to the nearest hundredth. blank cubic meters submit

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

We are given that \( r = 3 \) meters and \( h=9 \) meters. Substituting these values into the formula, we get \( V=\frac{1}{3}\pi(3)^{2}(9) \).

Step3: Simplify the expression

First, calculate \( (3)^{2}=9 \). Then the expression becomes \( V=\frac{1}{3}\pi\times9\times9 \). \( \frac{1}{3}\times9 = 3 \), so \( V = 3\times9\times\pi=27\pi \).

Step4: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( V\approx27\times3.14159 = 84.82293 \). Rounding to the nearest hundredth, we get \( 84.82 \).

Answer:

84.82