Given a radius [tex]r[/tex], the volume of a sphere is given by
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
We can solve this formula for the radius, given the volume:
[tex]r=\sqrt[3]{\dfrac{3V}{4\pi}}[/tex]
We can plug our value for the volume to get the radius:
[tex]r=\sqrt[3]{\dfrac{3\cdot 12\pi}{4\pi}}=\sqrt[3]{9}[/tex]
Answer:
[tex]\sqrt[3]{9}[/tex] or approximately 2.08 cm
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
12 pi = 4/3 pi r^3
Divide each side by pi
12 = 4/3 r^3
Multiply each side by 3/4
12 *3/4 = 3/4 * 4/3 r^3
9 = r^3
Take the cube root of each side
9 ^ 1/3 = r^3 ^ 1/3
9 ^ 1/3 = r
The radius is the cube root of 9
or approximately 2.080083823
