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The volume of a right cone is
144 pi units
^(3). If its height is 12 units, find its radius.
Answer: units

The volume of a right cone is $144 \pi$ units $^{3}$ . If its height is $12$ units, find its radius. $\newline$ Answer: units

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Circles: word problems

Full solution

Q. The volume of a right cone is

144 \pi

units

^{3}

. If its height is

12

units, find its radius.

\newline

Answer: units

Volume Formula Application: The formula for the volume of a right cone is $V = \frac{1}{3}\pi r^2 h$ , where $V$ is the volume, $r$ is the radius, and $h$ is the height of the cone. We are given that the volume $V$ is $144\pi$ units $^3$ and the height $h$ is $12$ units. We need to solve for $r$ .
Substitute Given Values: Let's plug in the given values into the volume formula: $144\pi = (\frac{1}{3})\pi r^2(12)$ .
Eliminate $\pi$ Term: To simplify the equation, we can divide both sides by $\pi$ to eliminate the $\pi$ term: $144 = \left(\frac{1}{3}\right)r^2(12)$ .
Multiply by $3$ : Next, we can multiply both sides by $3$ to get rid of the fraction: $144 \times 3 = r^2(12)$ .
Calculate Result: Now, we calculate $144 \times 3: 432 = r^2(12)$ .
Isolate $r^2$ : To isolate $r^2$ , we divide both sides by $12$ : $432 / 12 = r^2$ .
Calculate Square Root: We calculate $432 / 12$ : $36 = r^2$ .
Final Radius Calculation: To find $r$ , we take the square root of both sides: $r = \sqrt{36}$ .
Final Radius Calculation: To find $r$ , we take the square root of both sides: $r = \sqrt{36}$ . The square root of $36$ is $6$ , so $r = 6$ units.

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\newline

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\newline

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