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 demeter
To find the volume of a cylinder with a radius equal to the sphere and a height equal to the sphere's diameter, we need to first find the radius and diameter of the sphere.
The formula for the volume of a sphere is V = (4/3) * π * r^3, where V is the volume and r is the radius.
Given that the volume of the sphere is 48 m^3, we can set up the equation:
48 = (4/3) * π * r^3
To find the radius, we can rearrange the equation and solve for r:
r^3 = (3/4) * 48 / π
r^3 = 144 / π
r = (144 / π)^(1/3)
Now that we have the radius of the sphere, we can find its diameter:
d = 2 * r = 2 * (144 / π)^(1/3)
Finally, we can find the volume of the cylinder:
V_cylinder = π * r^2 * h
Hence, the volume of the cylinder with a radius equal to the sphere's and a height equal to the sphere's diameter is π * [(144 / π)^(1/3)]^2 * 2 * (144 / π)^(1/3).