A cone has a volume of 4710 cubic millimeters and a height of 20 millimeters. What is its radius? Use \( \pi \approx 3.14 \) and round your answer to the nearest hundredth. \( \quad r \approx \square \) millimeters

To find the radius of the cone, we can use the formula for the volume of a cone, which is given by: \[ V = \frac{1}{3} \pi r^2 h \] We know the volume \( V = 4710 \) mm³ and the height \( h = 20 \) mm. Rearranging the formula to solve for the radius \( r \): \[ 4710 = \frac{1}{3} \times 3.14 \times r^2 \times 20 \] First, we multiply both sides by 3 to eliminate the fraction: \[ 14130 = 3.14 \times r^2 \times 20 \] Next, we simplify: \[ 14130 = 62.8 \times r^2 \] Now, divide both sides by 62.8: \[ r^2 = \frac{14130}{62.8} \approx 224.44 \] Taking the square root of both sides: \[ r \approx \sqrt{224.44} \approx 15.00 \text{ mm} \] So, the radius \( r \approx 15.00 \) millimeters.