Respuesta :

LeonardoVivaldi
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.

The volume of a sphere is ​ 288π ​ cm³ so, the radius of the sphere is 6cm and this can be determined by using the formula of the sphere.

Given :

The volume of a sphere is ​ 288π ​ cm³.

The volume of the sphere is given by:

[tex]\rm V = \dfrac{4}{3}\pi r^3[/tex]    --- (1)

where r is the radius of the sphere and V denotes the volume of the sphere.

Now, put the value of V in the equation (1).

[tex]288\pi=\dfrac{4}{3}\pi r^3[/tex]

[tex]\sqrt[3]{ \dfrac{288\times 3 }{4}} = r[/tex]

r = 6 cm

The volume of a sphere is ​ 288π ​ cm³ so, the radius of the sphere is 6cm.

For more information, refer to the link given below:

https://brainly.com/question/21941816

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