Question

the volume of this cone is 678.24 cubic yards. what is the radius of this cone?
round your answer to the nearest hundredth.
18 yd
r ≈ □ yards

Explanation:

Step1: Recall cone volume formula

The volume \( V \) of a cone is \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is radius and \( h \) is height. From the diagram, \( h = 18 \) yd and \( V = 678.24 \) cubic yd.

Step2: Rearrange formula for \( r^2 \)

Multiply both sides by 3: \( 3V = \pi r^2 h \). Divide by \( \pi h \): \( r^2 = \frac{3V}{\pi h} \).

Step3: Substitute values

\( r^2 = \frac{3 \times 678.24}{\pi \times 18} = \frac{2034.72}{56.5487} \approx 35.98 \)

Step4: Calculate radius

Take square root: \( r = \sqrt{35.98} \approx 6.00 \)

Answer:

6.00