- #1

Rijad Hadzic

- 321

- 20

## Homework Statement

Find volume of the solid that lies above the cone Φ = π/3 and below the sphere ρ = 4cosΦ

## Homework Equations

## The Attempt at a Solution

Obviously this is a triple integral. My book tells me that 0 ≤ρ≤ 4cosΦ

but this makes no sense to me.

From the problem, it lies ABOVE the cone Φ = π/3 and below the sphere ρ = 4cosΦ, so wouldn't that imply that ρ is not starting at 0?

What I did was solved ρ = 4cosΦ

arccos(ρ/4) = Φ and set it = to pi/3

arccos(ρ/4) = π/3

ρ/4 = cosπ/3

ρ = 4 * (1/2) = 2

so wouldn't 2≤ρ≤4cosΦ be the bounds? I don't understand how the lower bound can start at 0 when its asking for what's above the cone and below the sphere..