The volume of this cone is 452.16 cubic feet. What is the height of this cone? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. The cone has a radius of 6 fee... The volume of this cone is 452.16 cubic feet. What is the height of this cone? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. The cone has a radius of 6 feet.
Understand the Problem
The question is asking us to find the height of a cone given its volume and radius. We will use the formula for the volume of a cone, which is V = (1/3) * pi * r^2 * h, and solve for h.
Answer
$h = 12.00$ feet
Answer for screen readers
$h = 12.00$ feet
Steps to Solve
- Write the formula for the volume of a cone
The formula for the volume $V$ of a cone with radius $r$ and height $h$ is: $$V = \frac{1}{3} \pi r^2 h$$
- Substitute the given values
We are given that $V = 452.16$ cubic feet and $r = 6$ feet. We are also told to use $\pi \approx 3.14$. Substituting these values into the formula: $$452.16 = \frac{1}{3} (3.14) (6^2) h$$
- Simplify the equation
Simplify the right side of the equation: $$452.16 = \frac{1}{3} (3.14) (36) h$$ $$452.16 = (3.14) (12) h$$ $$452.16 = 37.68 h$$
- Solve for h
Divide both sides of the equation by 37.68 to isolate $h$: $$h = \frac{452.16}{37.68}$$ $$h = 12$$
$h = 12.00$ feet
More Information
The height of the cone is exactly 12 feet. Therefore, rounding to the nearest hundredth, the answer is 12.00 feet.
Tips
A common mistake is forgetting to divide by 3 when using the volume of a cone formula. Also, errors can occur during the arithmetic, so it's important to double-check your calculations.
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