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The volume of a right cone is
343 pi units
^(3). If its height is 21 units, find its radius.
Answer: units

The volume of a right cone is $343 \pi$ units $^{3}$ . If its height is $21$ units, find its radius. $\newline$ Answer: units

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Circles: word problems

Full solution

Q. The volume of a right cone is

343 \pi

units

^{3}

. If its height is

21

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 the volume $V = 343\pi$ units $^3$ and the height $h = 21$ units. We need to solve for the radius $r$ .
Substitute Given Values: First, let's plug in the given values into the volume formula: $343\pi = (\frac{1}{3})\pi r^2(21)$ .
Simplify Equation: To solve for $r^2$ , we can simplify the equation by dividing both sides by $\pi$ , which gives us $343 = (\frac{1}{3})r^2(21)$ .
Eliminate Fraction: Next, we can multiply both sides by $3$ to get rid of the fraction: $3 \times 343 = r^2(21)$ .
Calculate Value: Now, we calculate $3 \times 343$ , which equals $1029$ . So, we have $1029 = r^2(21)$ .
Isolate $r^2$ : To isolate $r^2$ , we divide both sides by $21$ : $\frac{1029}{21} = r^2$ .
Calculate Square Root: Calculating $1029 / 21$ gives us $49 = r^2$ .
Final Radius Calculation: Finally, to find $r$ , we take the square root of both sides: $\sqrt{49} = r$ .
Final Radius Calculation: Finally, to find $r$ , we take the square root of both sides: $\sqrt{49} = r$ .The square root of $49$ is $7$ , so $r = 7$ units.

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\newline

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