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MATH SOLVE
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The volume of a sphere is 288π cm³. what is the radius of the sphere? enter your answer in the b...
4 months ago
Q:
The volume of a sphere is 288π cm³. what is the radius of the sphere? enter your answer in the box. cm
Accepted Solution
A:
Answer: 6 cm
Explanation:
Let r = radius of the sphere. Then, the volume of the sphere is given by
Volume = [tex]\frac{4}{3} \pi r^3[/tex] (1)
Since the volume is 288π cm³, equation (1) becomes
[tex]288 = \frac{4}{3} \pi r^3 \newline \indent \frac{4}{3} \pi r^3 = 288\pi \newline \indent \frac{4\pi r^3}{3} = 288\pi \newline \indent 3\left (\frac{4\pi r^3}{3} \right ) = 3(288\pi) \newline \newline \indent 4\pi r^3 = 864\pi \newline \newline \indent \frac{4\pi r^3}{4\pi} = \frac {864\pi}{4\pi} \newline \newline \indent r^3 = 216 \newline \indent r = \sqrt[3]{216} \newline \indent \boxed{r = 6} [/tex]
Hence, the radius is 6 cm.