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 18 cm3 18 cm cubed 12 cm3 12 cm cubed 24 cm3 24 cm cubed 54 cm3
Given that the volume of a cylinder is 36 cm3, we can use the formula for the volume of a cylinder to find the radius.
The formula for the volume of a cylinder is V = πr2h, where V is the volume, r is the radius, and h is the height.
Since the volume is 36 cm3 and the height is equal to the diameter of the sphere, we have:
36 = πr2(2r)
36 = 2πr3
r3 = 18/π
r ≈ 2.41 cm
Now that we have the radius of the cylinder, we can use it to find the volume of the sphere using the formula V = 4/3πr3:
V = 4/3(π)(2.41)3
V ≈ 18 cm3
So, the volume of the sphere is 18 cm3.