Question

the volume of this cone is 753.6 cubic millimeters. what is the radius of this cone? round your answer to the nearest hundredth. 20 mm r ≈ millimeters

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, \( h = 20 \, \text{mm} \), \( V = 753.6 \, \text{mm}^3 \).

Step2: Rearrange 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

\( r^2 = \frac{3 \times 753.6}{\pi \times 20} = \frac{2260.8}{62.8319} \approx 35.98 \).

Step4: Calculate \( r \)

Take square root: \( r \approx \sqrt{35.98} \approx 5.998 \approx 6.00 \).

Answer:

6.00