The volume of a sphere is 48 m^3 what is the volume of a cylinder if its 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. We are given that the volume of the sphere is 48 m^3.
48 = (4/3)πr^3
To find the radius of the sphere, we can rearrange the equation:
r^3 = (3/4)(48/π)
r^3 = 36
r = ∛36 ≈ 3.301 m (rounded to 3 decimal places)
The radius of the cylinder is also given as 3.301 m.
Now, let's find the height of the cylinder. We are given that the height is equal to the sphere's diameter, which is twice the radius:
Height of cylinder = 2 * r ≈ 2 * 3.301 m = 6.602 m (rounded to 3 decimal places)
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Volume of cylinder = π * (3.301 m)^2 * 6.602 m
≈ π * 10.888 m^2 * 6.602 m
≈ 226.195 m^3 (rounded to 3 decimal places)
Therefore, the volume of the cylinder is approximately 226.195 m^3.