Question

a cone has a height of 18 yards and a radius of 15 yards. what is its volume? round your answer to the nearest hundredth. cubic yards

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 \( r = 15 \) yards and \( h=18 \) yards. Substituting these values into the formula, we get:
\( V=\frac{1}{3}\pi\times(15)^{2}\times18 \)
First, calculate \( (15)^{2}=225 \). Then, \( \frac{1}{3}\times225\times18 \). \( \frac{1}{3}\times225 = 75 \), and \( 75\times18=1350 \). So now the formula becomes \( V = 1350\pi \)

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( V\approx1350\times3.14159 \)
\( 1350\times3.14159 = 4241.1465 \)
Rounding to the nearest hundredth, we get \( 4241.15 \)

Answer:

\( 4241.15 \)