The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * r^3
Where r is the radius of the sphere.
We are given that the volume of the sphere is 48 m^3, so we can set up the following equation:
48 = (4/3) * π * r^3
Simplifying the equation:
r^3 = (3/4) * 48 / π
r^3 = 36 / π
r = (36 / π)^(1/3)
Since the radius of the cylinder is the same as the sphere, the radius of the cylinder would also be (36 / π)^(1/3).
The height of the cylinder is given as the sphere's diameter. Diameter = 2 * radius, so the height of the cylinder would be 2 * (36 / π)^(1/3).
Now we can calculate the volume of the cylinder using the formula:
V_cylinder = π * r^2 * h
Substituting the values:
V_cylinder = π * (36 / π)^(1/3)^2 * 2 * (36 / π)^(1/3)
= 2 * π * (36 / π)^(2/3) * (36 / π)^(1/3)
= 2 * π * (36 / π)
= 2 * 36
= 72 m^3
Therefore, the volume of the cylinder is 72 m^3.
The volume of a sphere is 48 m3 . What is the volume of a cylinder if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?
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