Calculate the radius of a sphere with a volume of 36π.

To determine the radius of a sphere given its volume of ( 36\pi ), we can use the formula for the volume of a sphere, which is:

[

V = \frac{4}{3} \pi r^3

]

where ( V ) is the volume and ( r ) is the radius of the sphere. Given that the volume ( V ) is ( 36\pi ), we can set up the equation as follows:

[

\frac{4}{3} \pi r^3 = 36 \pi

]

To eliminate ( \pi ) from both sides of the equation, we divide by ( \pi ):

[

\frac{4}{3} r^3 = 36

]

Next, we multiply both sides by ( \frac{3}{4} ) to isolate ( r^3 ):

[

r^3 = 36 \times \frac{3}{4}

]

[

r^3 = 27

]

Now, we find the value of ( r ) by taking the cube root of both sides:

[

r = \sqrt[3]{27}

]

[

r