To find the volume of the cylinder, we need to know the radius of the sphere. Since the radius of both the sphere and the cylinder are the same, we can denote it as r.
The formula for the volume of a sphere is V_sphere = (4/3) * π * r^3.
We are given that the volume of the sphere is 48 m^3. Hence,
48 = (4/3) * π * r^3.
Now, let's solve this equation to find the value of r:
48 / ((4/3) * π) = r^3.
r^3 = 36 / π.
Taking the cube root of both sides:
r = (36 / π)^(1/3).
Now, we know the value of the radius, so we can calculate the diameter of the sphere which is twice the radius:
d = 2r = 2 * (36 / π)^(1/3).
The height of the cylinder is given as the diameter of the sphere, which is d. So,
height_cylinder = d = 2 * (36 / π)^(1/3).
The formula for the volume of a cylinder is V_cylinder = π * r^2 * height_cylinder.
Now, we can substitute the values:
V_cylinder = π * ((36 / π)^(1/3))^2 * (2 * (36 / π)^(1/3)).
Simplifying this expression will give the volume of the cylinder.
The volume of a sphere is 48 m^3, what is the volume of a cylinder if it's radius is the same as the Spheres and its height is equal to the Spheres diameter?
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