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)
○ 12 cm³
○ 24 cm³
○ 18 cm³
○ 54 cm³
First, we need to find the radius and height of the cylinder based on the given volume. 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.
Given that the volume of the cylinder is 36 cm³, we can set up the equation as:
36 = πr²h
Since the height of the cylinder is equal to the diameter of the sphere, we have h = 2r.
Substitute h = 2r into the equation:
36 = πr²(2r)
36 = 2πr³
r³ = 18/π
r = (18/π)^(1/3)
r ≈ 2.54 cm
Now that we have the radius of the cylinder, we can find the volume of the sphere using the formula V = (4/3)πr³:
V = (4/3)π(2.54)³
V ≈ 54 cm³
Therefore, the volume of the sphere is approximately 54 cm³. So, the answer is 54 cm³.