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

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To find the radius of the cone, we can use the formula for the volume of a cone:

$$ V = \frac{1}{3} \pi r^2 h $$

Given:
- Volume of the cone, $$ V = 4710 $$ cubic millimeters
- Height of the cone, $$ h = 20 $$ millimeters
- Approximation of $$ \pi $$ as 3.14

We can substitute the given values into the formula and solve for the radius $$ r $$.
Solve the equation $$ 4710 = \frac{1}{3} \times 3.14 \times r^{2} \times 20 $$.
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
  $$4710=\frac{1}{3}\times 3.14r^{2}\times 20$$
- step1: Multiply the terms:
  $$4710=\frac{314}{15}r^{2}$$
- step2: Swap the sides:
  $$\frac{314}{15}r^{2}=4710$$
- step3: Divide both sides:
  $$\frac{\frac{314}{15}r^{2}}{\frac{314}{15}}=\frac{4710}{\frac{314}{15}}$$
- step4: Divide the numbers:
  $$r^{2}=225$$
- step5: Simplify the expression:
  $$r=\pm \sqrt{225}$$
- step6: Simplify the expression:
  $$r=\pm 15$$
- step7: Separate into possible cases:
  $$\begin{align}&r=15\&r=-15\end{align}$$
- step8: Rewrite:
  $$r_{1}=-15,r_{2}=15$$
The solutions to the equation are $$ r = -15 $$ and $$ r = 15 $$. Since the radius cannot be negative, the radius of the cone is approximately 15 millimeters.
The radius of the cone is approximately 15.00 millimeters.

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

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