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
12 cm3
12 cm cubed
54 cm3
In order to solve this problem, we need to use the relationship between the formulas for the volumes of a cylinder and a sphere.
The volume of a cylinder is given by the formula Vcylinder = πr^2h, where r is the radius and h is the height.
The volume of a sphere is given by the formula Vsphere = (4/3)πr^3, where r is the radius.
We are given that the volume of the cylinder is 36 cm^3. Let's say the radius of the cylinder and sphere is 'r' and the height of the cylinder is '2r' (since the height of the cylinder is equal to the diameter of the sphere).
Substituting these values into the volume formula for the cylinder, we get:
36 = πr^2 * 2r
Simplifying this equation, we have:
18 = πr^3
Now we can compare this equation with the formula for the volume of a sphere. By comparing the two equations, we can see that the volume of the sphere is also equal to 18 cm^3.
Therefore, the correct answer is: 18 cm3 or 18 cm cubed.