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The volume of a right cone is
27 pi units
^(3). If its height is 9 units, find its radius.
Answer: units

The volume of a right cone is $27 \pi$ units $^{3}$ . If its height is $9$ units, find its radius. $\newline$ Answer: units

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Circles: word problems

Full solution

Q. The volume of a right cone is

27 \pi

units

^{3}

. If its height is

9

units, find its radius.

\newline

Answer: units

Recall Cone Volume Formula: Recall the formula for the volume of a cone. $\newline$ The formula for the volume of a cone is $V = \frac{1}{3}\pi r^2 h$ , where $V$ is the volume, $r$ is the radius, and $h$ is the height.
Plug in Given Values: Plug in the given values for the volume and height into the formula. $\newline$ We know the volume $V$ is $27\pi$ units $^3$ and the height $h$ is $9$ units. So, we have $27\pi = (\frac{1}{3})\pi r^2(9)$ .
Simplify Equation: Simplify the equation to solve for $r^2$ . First, we can cancel $\pi$ from both sides of the equation, which gives us $27 = (\frac{1}{3})r^2(9)$ . Then, we simplify the right side by multiplying $(\frac{1}{3})$ by $9$ , which gives us $27 = 3r^2$ .
Isolate $r^2$ : Divide both sides of the equation by $3$ to isolate $r^2$ . $\newline$ Dividing both sides by $3$ gives us $9 = r^2$ .
Solve for $r$ : Take the square root of both sides to solve for $r$ . The square root of $9$ is $3$ , so $r = 3$ units.

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\newline

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1

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One of the legs of a right triangle measures

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\newline

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Question

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\newline

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