The volume of a cone is 56.52 cubic millimeters and its height is 6 mm. Using π ≈ 3.14, what is the radius of the cone, rounded to the nearest hundredth?
Understand the Problem
The question provides the volume and height of a cone, and asks us to calculate the radius of the cone. We will use the formula for the volume of a cone (V = 1/3 * pi * r^2 * h) and rearrange it to solve for the radius r, plugging in the given volume V and height h. Remember to use 3.14 as the value for pi.
Answer
$r = 3.00$
Answer for screen readers
$r = 3.00$
Steps to Solve
- State the formula for the volume of a cone
The volume $V$ of a cone is given by the formula: $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius and $h$ is the height.
- Plug in the given values
We are given that the volume $V = 56.52$ cubic millimeters, the height $h = 6$ mm, and we are told to use $\pi \approx 3.14$. Plugging these values into the formula gives: $$56.52 = \frac{1}{3} (3.14) r^2 (6)$$
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Simplify the equation $$56.52 = (3.14) r^2 (2)$$ $$56.52 = 6.28 r^2$$
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Solve for $r^2$
Divide both sides of the equation by 6.28: $$r^2 = \frac{56.52}{6.28} = 9$$
- Solve for $r$
Take the square root of both sides of the equation: $$r = \sqrt{9} = 3$$
$r = 3.00$
More Information
The radius of the cone is exactly 3 mm. Since we are asked to round to the nearest hundredth, we write 3.00 mm.
Tips
A common mistake is to incorrectly rearrange the formula for the volume of a cone when solving for the radius. Also, forgetting to take the square root to find $r$ after finding $r^2$ is a frequent error. Another error is using the incorrect order of operations to simplify the equation. Finally, not rounding to the nearest hundredth as requested.
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