Find the volume of the cone. Round your answer to the nearest whole number.

1. Height: 2.75 m
Volume: \(46^{3}\) m

1 answer

To find the volume of a cone, you can use the formula:

\[ V = \frac{1}{3} \times \pi \times r^2 \times h \]

Given that the volume of the cone is \(46^{3} \, m\), we can set up the equation as:

\[ 46^{3} = \frac{1}{3} \times \pi \times r^2 \times 2.75 \]

Solving for \(r^2\):

\[ r^2 = \frac{3 \times 46^{3}}{\pi \times 2.75} \]

\[ r^2 \approx 11669.32 \]

Taking the square root of \(11669.32\), we get:

\[ r \approx 108 \, m \]

Now, plugging the values of \(r = 108 \, m\) and \(h = 2.75 \, m\) back into the volume formula:

\[ V = \frac{1}{3} \times \pi \times 108^2 \times 2.75 \]

\[ V \approx 10802 \, m^{3} \]

Therefore, the volume of the cone is approximately \(10802 \, m^{3}\).