Question

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

24 cm3
24 cm cubed

18 cm3
18 cm cubed

54 cm3
54 cm cubed

12 cm3

Answer 1

[AI-generated answer — Bot GPT 3.5]

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

Given that the volume of the cylinder is 36 cm^3, V = 36 cm^3.

Since the height of the cylinder is equal to the diameter of the sphere, h = 2r.

Substitute h = 2r into the formula for the volume of a cylinder:

36 = πr^2(2r)
36 = 2πr^3
r^3 = 18/π
r = (18/π)^(1/3) ≈ 2.45 cm

Now, we can find the volume of a sphere using the formula V = (4/3)πr^3:

V = (4/3)π(2.45)^3
V ≈ 24 cm^3

Therefore, the volume of the sphere is 24 cm^3.