Since the volume of the cylinder is 36 cm^3, we can use the formula V = πr^2h for the volume of a cylinder. If the radius of the cylinder is r, and the height is h (the same as the diameter of the sphere), we have:
36 = πr^2h
Since h = 2r (diameter of the sphere), we have:
36 = πr^2(2r)
36 = 2πr^3
18 = πr^3
Now, to find the volume of the sphere, we use the formula V = (4/3)πr^3:
V = (4/3)πr^3
V = (4/3)π(18)
V = 24 cm^3
Therefore, the volume of the sphere is 24 cm^3.
The answer is: 24 cm^3
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
18 cm3
18 cm cubed
12 cm3
12 cm cubed
24 cm3
24 cm cubed
54 cm3
1 answer
1 answer