A sphere fits exactly into a cylindrical. The volume of the cylinder is 30cm cube. What is the volume of the sphere?

Answer 1

The assumption here is that the cylinder's height is the same as its diameter

h = d

The formula for the volume of a cylinder is:

r² * π * h

Since 2r = d and h = d we can substitute h with 2r:

r² * π * 2r

Now we can add the 30 cm³ to the equation and solve for r:

r² * π * 2r = 30 | /π

r² * 2r = 30 / π | simplify on the left

2r³ = 30 / π | /2

r³ = 30 / 2π

r = ³√(30 / 2π)

r = 1.6838

Now for the sphere. The formula for the volume of a sphere is:

v = 4/3 * π * r³

Substitute r with 1.6838 and solve:

v = 4/3 * π * 1.68383

v = 20