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 54 cm3 54 cm cubed 24 cm3 24 cm cubed 12 cm3 12 cm cubed 18 cm3
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Given that the volume of the cylinder is 36 cm^3, we can write the equation as:
36 = πr^2h
The height of the cylinder is equal to the diameter of the sphere, so h = 2r.
Substituting this into the equation, we get:
36 = πr^2(2r)
36 = 2πr^3
18 = πr^3
To find the volume of the sphere, we use the formula V = (4/3)πr^3.
Substituting the value of πr^3 from the previous equation, we get:
V = (4/3)(18)
V = 24 cm^3
Therefore, the volume of the sphere is 24 cm^3.