The volume of a cylinder is given by the formula Vcylinder = πr²h, where r is the radius and h is the height.
In this case, we are given that the volume of the cylinder is 36 cm^3, so we can write the equation as 36 = πr²h.
The volume of a sphere is given by the formula Vsphere = (4/3)πr³, where r is the radius.
We are told that the radius of the sphere is the same as the cylinder's radius, so let's call it r as well.
We are also told that the height of the cylinder is equal to the sphere's diameter, which means that h = 2r.
Substituting this information into the equation for the volume of the cylinder, we get:
36 = πr²(2r)
36 = 2πr³
18 = πr³
Now we can substitute this value of πr³ into the equation for the volume of the sphere:
Vsphere = (4/3)πr³
Vsphere = (4/3)(18)
Vsphere = 24 cm^3
Therefore, the volume of the sphere with the same radius as the cylinder and height equal to the sphere's diameter 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
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