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The volume of a right cone is
1680 pi units
^(3). If its radius measures 12 units, find its height.
Answer: units

The volume of a right cone is $1680 \pi$ units $^{3}$ . If its radius measures $12$ units, find its height. $\newline$ Answer: units

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Circles: word problems

Full solution

Q. The volume of a right cone is

1680 \pi

units

^{3}

. If its radius measures

12

units, find its height.

\newline

Answer: units

Write Volume Formula: 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 the volume $V = 1680\pi$ units $^3$ and the radius $r = 12$ units. We need to solve for the height $h$ .
Substitute Known Values: First, let's plug the known values into the volume formula: $1680\pi = \left(\frac{1}{3}\right)\pi(12)^2h$ .
Simplify Equation: Next, we simplify the right side of the equation by squaring the radius: $1680\pi = (\frac{1}{3})\pi(144)h$ .
Cancel $\pi$ : Now, we can cancel $\pi$ from both sides of the equation, which gives us $1680 = (1/3)(144)h$ .
Isolate Term with $h$ : We multiply both sides of the equation by $3$ to isolate the term with $h$ : $5040 = 144h$ .
Solve for h: Finally, we divide both sides by $144$ to solve for $h$ : $h = \frac{5040}{144}$ .
Final Height: After performing the division, we find that $h = 35$ units.

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