The volume of a sphere is 48m ^ 3 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? (1 point) m ^ 3
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 of the sphere.
Given that the volume of the sphere is 48 m^3, we can set up the equation:
48 = (4/3)πr^3
To find the volume of the cylinder, we need to find the radius and height of the cylinder. Since the radius of the cylinder is the same as the sphere's, we can substitute r in the equation:
48 = (4/3)π(r^3)
Now, let's find the value of r:
48 * (3/4)π = r^3
36π = r^3
To find the radius, we can take the cube root of both sides:
r = ∛(36π)
Now, the height of the cylinder is equal to the diameter of the sphere, which is twice the radius:
Height = 2 * r = 2 * ∛(36π)
Finally, we can use the formula for the volume of a cylinder to find the volume:
V_cylinder = πr^2 * h
V_cylinder = π(∛(36π))^2 * 2 * ∛(36π)
Therefore, the volume of the cylinder is expressed in m^3.