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An orange is in the shape of a sphere. Its volume is
288 pi cubic centimeters. What is the radius of the orange, in centimeters?

An orange is in the shape of a sphere. Its volume is $288 \pi$ cubic centimeters. What is the radius of the orange, in centimeters?

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Pythagorean Theorem and its converse

Full solution

Q. An orange is in the shape of a sphere. Its volume is

288 \pi

cubic centimeters. What is the radius of the orange, in centimeters?

Write formula for volume: Write down the formula for the volume of a sphere. $\newline$ The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$ , where $V$ is the volume and $r$ is the radius.
Set given volume equal: Set the given volume equal to the formula for the volume of a sphere. $\newline$ We know the volume $V$ is $288\pi$ cubic centimeters, so we set this equal to the formula: $288\pi = \left(\frac{4}{3}\right)\pi r^3$ .
Solve for r^ $3$ : Solve for r^ $3$ by isolating it on one side of the equation. $\newline$ To isolate r^ $3$ , we divide both sides of the equation by $(\frac{4}{3})\pi$ : $\frac{288\pi}{(\frac{4}{3})\pi} = r^3$ .
Simplify equation to solve: Simplify the equation to solve for $r^3$ . $\newline$ The $\pi$ on both sides cancels out, and we are left with: $\frac{288}{\frac{4}{3}} = r^3$ .
Calculate value of r^ $3$ : Calculate the value of $r^3$ . $\newline$ To simplify $(288) / (\frac{4}{3})$ , we multiply $288$ by the reciprocal of $(\frac{4}{3})$ , which is $(\frac{3}{4})$ : $288 \times (\frac{3}{4}) = r^3$ .
Perform multiplication to find $r^3$ : Perform the multiplication to find the value of $r^3$ . $\newline$ Calculating $288 \times \left(\frac{3}{4}\right)$ gives us: $216 = r^3$ .
Take cube root to solve for $r$ : Take the cube root of both sides to solve for $r$ . $\newline$ To find $r$ , we take the cube root of $216$ : $r = \sqrt[$ $3$ ]{ $216$ }.
Calculate cube root to find radius: Calculate the cube root of $216$ to find the radius. $\newline$ The cube root of $216$ is $6$ , so $r = 6$ centimeters.

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