The volume of a sphere is 48 M cubed 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
To find the volume of a cylinder, we need to know the radius and height. If the radius of the cylinder is the same as the sphere's radius, then we can use the given information.
As we know, the formula for the volume of a sphere is given by V_sphere = (4/3)πr³, where r is the radius.
From the given information, V_sphere = 48 m³.
Setting up the equation, we have:
48 = (4/3)πr³
To find the radius (r), we can solve for it:
48 * (3/4π) = r³
36π = r³
Taking the cube root of both sides, we have:
r = ∛(36π)
Now, since the height of the cylinder is equal to the sphere's diameter, which is twice the radius, we have:
height = 2r
Substituting the value of r, we get:
height = 2 * ∛(36π)
Therefore, the volume (V_cylinder) of this cylinder can be obtained using the formula V_cylinder = πr² * height:
V_cylinder = π * (∛(36π))² * (2 * ∛(36π))
Simplifying this expression will provide the exact value of the cylinder's volume.