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 18 cm3 18 cm cubed 54 cm3 54 cm cubed 24 cm3
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius.
In this problem, it is given that the volume of the cylinder is 36 cm^3.
Let's say the radius of the cylinder and the sphere is "r".
It is also given that the height of the cylinder is equal to the diameter of the sphere, which means h = 2r.
Substituting these values in the formula for the volume of a cylinder:
36 = πr^2(2r)
36 = 2πr^3
Divide both sides of the equation by 2π:
18 = r^3
Now substitute this value of r^3 in the formula for the volume of a sphere:
V = (4/3)πr^3
V = (4/3)π(18)
V = 24π cm^3
So, the volume of the sphere is 24π cm^3, which is approximately equal to 75.4 cm^3 (rounded to 1 decimal place).
Therefore, the correct answer is 24 cm^3.