Use the relationship among the formulas for the volumes of cones, cylinders, and spheres to solve the following problem. The volume of a cylinder is 36 cm3 . What is the volume of a sphere if its radius is the same as the cylinder’s and the height of the cylinder is equal to the sphere’s diameter?(1 point) Responses 12 cm3 12 cm cubed 24 cm3 24 cm cubed 54 cm3 54 cm cubed 18 cm3
First, find the radius and height of the cylinder:
Let the radius be r and the height be h.
Given the volume of the cylinder is 36 cm3, we have:
V = πr2h = 36
Since the height of the cylinder is equal to the sphere's diameter, h = 2r.
Substitute this into the equation:
πr2(2r) = 36
2πr3 = 36
r3 = 18
r = ∛18 ≈ 2.62 cm
Now, we can find the volume of the sphere using the formula for the volume of a sphere:
V = (4/3)πr3
Substitute the radius:
V = (4/3)π(2.62)3 ≈ 54 cm3
Therefore, the volume of the sphere is 54 cm3.