Question

Which equation and solution give the radius of the smaller cylinder if the volume inside the larger cylinder but out side the smaller cylinder is 768 centimeter

Answer 1

`768\pi = 1024\pi - 16\pi r^2`

`r = 4`

Explanation:

See attachment for complete question

Given

`v = 1.024\pi - 16\pi r^2`

Required

Determine the equation and solution when v = 768

`v = 1024\pi - 16\pi r^2`

Substitute
`768\pi` for v

`768\pi = 1024\pi - 16\pi r^2`

The above expression represents the equation

Solving further:

`768\pi = 1024\pi - 16\pi r^2`

Collect like terms

`16\pi r^2 = 1024\pi - 768\pi`

`16\pi r^2 = 256\pi`

Divide both sides by
`16\pi`

`r^2 = (256\pi)/(16\pi)`

`r^2 = (256)/(16)`

`r^2 = 16`

Take square roots of both sides

`r = \sqrt{16`

`r = 4`