Since volume of a sphere(V) = [tex]\frac{4 \pi r^3}{3}[/tex]
V = [tex]\frac{4 \pi r^3}{3}[/tex]
[tex]r =( {\frac{3V}{4 \pi}})^ \frac{1}{3}[/tex]
So, the relationship between the radius and volume of sphere is given by [tex]r =( {\frac{3V}{4 \pi}})^ \frac{1}{3}[/tex].
Now, it is given that the volume of sphere is [tex]36 \pi[/tex] cubic units. we have to determine the radius of the sphere.
[tex]r =( {\frac{3 \times 36 \pi}{4 \pi}})^ \frac{1}{3}[/tex]
Cancelling [tex]\pi[/tex] from numerator and denominator, we get
[tex]r =( {\frac{3 \times 36}{4}})^ \frac{1}{3}[/tex]
[tex]r =( {{3 \times 9})^ \frac{1}{3}[/tex]
[tex]r =( {27})^ \frac{1}{3}[/tex]
[tex]r =( {3^3})^ \frac{1}{3}[/tex]
So, r = 3 units
Therefore, the radius of the sphere is 3 units.
