The volume of a cone is 47.1 cubic millimeters and its radius is 3mm. What is the height of the cone? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth.
Understand the Problem
The question provides the volume and radius of a cone and asks to calculate the height of the cone. We will use the formula for the volume of a cone, $V = (1/3) * \pi * r^2 * h$, where V is the volume, r is the radius, and h is the height. Then we will isolate for h and solve to determine the height of the cone.
Answer
$h = 5.00$
Answer for screen readers
$h = 5.00$
Steps to Solve
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Write down the formula for the volume of a cone. The formula for the volume of a cone is: $V = \frac{1}{3} \pi r^2 h$
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Plug in the given values. We know that $V = 47.1$ cubic millimeters, $r = 3$ mm, and $\pi \approx 3.14$. So, we have: $47.1 = \frac{1}{3} (3.14) (3^2) h$
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Simplify the equation. $47.1 = \frac{1}{3} (3.14) (9) h$ $47.1 = (3.14) (3) h$ $47.1 = 9.42 h$
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Solve for h. Divide both sides by 9.42: $h = \frac{47.1}{9.42}$ $h = 5$
$h = 5.00$
More Information
The height of the cone is exactly 5 millimeters. Since the question asked us to round to the nearest hundredth, we write it as 5.00 mm.
Tips
A common mistake is using the incorrect formula for the volume of a cone or making a mistake when substituting the values into the formula. Another common mistake is not rounding to the specified decimal place in the problem.
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