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The volume of a right cone is
1344 pi units
^(3). If its diameter measures 24 units, find its height.
Answer: units

The volume of a right cone is $1344 \pi$ units $^{3}$ . If its diameter measures $24$ units, find its height. $\newline$ Answer: units

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The volume of a right cone is

1344 \pi

units

^{3}

. If its diameter measures

24

units, find its height.

\newline

Answer: units

Identify Given Information: Identify the given information and the formula for the volume of a cone. $\newline$ The volume $V$ of a cone is given by the formula $V = \frac{1}{3}\pi r^2 h$ , where $r$ is the radius and $h$ is the height. $\newline$ Given volume $V = 1344\pi$ cubic units and diameter $d = 24$ units, we can find the radius $r$ by dividing the diameter by $2$ .
Calculate Radius: Calculate the radius of the cone. $\newline$ Radius $r = \frac{d}{2} = \frac{24 \text{ units}}{2} = 12 \text{ units}.$
Substitute Values and Solve: Substitute the values of the volume and radius into the volume formula and solve for the height $h$ . $\newline$ $1344\pi = \left(\frac{1}{3}\right)\pi(12^2)h$
Simplify Equation: Simplify the equation by dividing both sides by $\pi$ and multiplying by $3$ to isolate $h$ . $\newline$ $1344 = (\frac{1}{3})(12^2)h$ $\newline$ $1344 \times 3 = 12^2 \times h$ $\newline$ $4032 = 144h$
Divide to Solve for Height: Divide both sides by $144$ to solve for $h$ . $\newline$ $h = \frac{4032}{144}$ $\newline$ $h = 28 \text{ units}$

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