The volume of a sphere is 48m^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 diameter
The volume of a sphere is given by the formula: V = (4/3)πr^3, where r is the radius of the sphere.
Here, the volume of the sphere is given as 48m^3. So, we have 48 = (4/3)πr^3.
Let's solve this equation to find the radius, r, of the sphere.
48 = (4/3)πr^3
Divide both sides by (4/3)π:
48 / ((4/3)π) = r^3
Multiply both sides by (3/4)π:
(3/4)π * 48 / ((4/3)π) = (3/4) * r^3
(3/4)*(3/4)*r^3 = (3/4) * r^3
r^3 = (3/4)*(3/4)*48
r^3 = (9/16)*48
r^3 = 27
Taking the cube root of both sides, we find:
r = 3
So, the radius of the sphere is 3m.
Now, let's find the volume of the cylinder.
The volume of a cylinder is given by the formula: V = πr^2h, where r is the radius and h is the height of the cylinder.
Given that the radius of the cylinder is the same as the sphere (r = 3m) and the height of the cylinder is equal to the sphere's diameter (2r = 2*3 = 6m), we can calculate the volume of the cylinder as follows:
V = π(3^2)(6) = 9π(6) = 54π
So, the volume of the cylinder is 54π cubic meters.