The volume of a sphere is 48 m cubed what is the volume of the cylinder if the radius is the same as the spheres and its height is equal to the spheres diameter
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
Given that the volume of the sphere is 48 m³, we can set up the following equation:
48 = (4/3)πr^3
To find the radius, we need to rearrange the equation:
r^3 = (3/4)(48/π)
Simplifying the right side:
r^3 = 36
Taking the cube root of both sides:
r = 3 meters
Now, we need to find the volume of the cylinder. The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Since the height of the cylinder is equal to the sphere's diameter, it means the height is twice the radius of the sphere. Thus, h = 2r = 2(3) = 6 meters.
Substituting the radius and height values into the formula:
V = π(3^2)(6)
V = π(9)(6)
V = 54π
So, the volume of the cylinder is 54π cubic meters.