A cylinder has a volume of $405\pi$ cubic meters. What is its height if the radius is 9 meters?
Understand the Problem
The question asks us to find the height of a cylinder given its volume and radius. We are given that the volume of the cylinder is $405\pi$ cubic meters and the radius is 9 meters. We need to use the formula for the volume of a cylinder, $V = \pi r^2 h$, and solve for $h$.
Answer
$h = 5$
Answer for screen readers
$h = 5$
Steps to Solve
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Write down the formula for the volume of a cylinder. The formula for the volume of a cylinder is: $$V = \pi r^2 h$$
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Plug in the given values. We are given that $V = 405\pi$ cubic meters and $r = 9$ meters. Plugging these values into the formula, we get: $$405\pi = \pi (9)^2 h$$
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Simplify the equation. Simplify the equation by squaring 9: $$405\pi = \pi (81) h$$ $$405\pi = 81\pi h$$
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Solve for $h$. Divide both sides of the equation by $81\pi$ to isolate $h$: $$\frac{405\pi}{81\pi} = \frac{81\pi h}{81\pi}$$ $$h = \frac{405\pi}{81\pi}$$
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Calculate the height. Simplify the fraction by dividing both the numerator and denominator by $\pi$: $$h = \frac{405}{81}$$ Now divide 405 by 81: $$h = 5$$
$h = 5$
More Information
The height of the cylinder is 5 meters.
Tips
A common mistake is to forget to square the radius in the formula $V = \pi r^2 h$. Another mistake is to incorrectly divide or simplify the fraction when solving for $h$.
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