1 answer
(click or scroll down)
First, we need to find the radius and height of the cylinder. Since the volume of the cylinder is 36 cm^3 and the formula for the volume of a cylinder is V = πr^2h, we can set up the following equation:
36 = πr^2h
Since the height of the cylinder is equal to the sphere's diameter, which is twice the radius of the sphere, we can write h = 2r. Substituting this into the equation above, we get:
36 = πr^2(2r)
36 = 2πr^3
r^3 = 18/π
r = ∛(18/π)
r ≈ 1.64 cm
Now that we have found the radius of the cylinder, we can use it to find the volume of the sphere. The formula for the volume of a sphere is V = (4/3)πr^3. Substituting the radius we found earlier, we get:
V = (4/3)π(1.64)^3
V ≈ 18 cm^3
Therefore, the closest answer choice is C.) 18 cm^3.