Use the relationship among the formulas for the volumes of cones, cylinders, and spheres to the following problemThe volume of a cylinder is 36c * m ^ 3 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? (point )
The volume of a cylinder is given by the formula Vcylinder = πr^2h, where r is the radius of the base and h is the height of the cylinder.
Given that the volume of the cylinder is 36c*m^3, we can substitute this value into the formula:
36c*m^3 = πr^2h
We are also given that the height of the cylinder is equal to the sphere's diameter. Since the diameter of a sphere is twice the radius, we can say that h = 2r.
Substituting this into the equation, we have:
36c*m^3 = πr^2(2r)
Simplifying, we get:
36c*m^3 = 2πr^3
To find the volume of a sphere, we use the formula Vsphere = (4/3)πr^3. The radius of the sphere is the same as the radius of the cylinder, so we can say:
Vsphere = (4/3)πr^3
Comparing this with the equation above, we see that the volume of the sphere is equal to half of the volume of the cylinder. Hence, the volume of the sphere is:
Vsphere = 36c*m^3 / 2