Finding the Integral Limits for an Inverted Cone Body

[unscientific]

Homework Statement

The problem is attached in the picture.

The Attempt at a Solution

My question is, why can't the limits of ∫(dp) be from 0 to 1?

The shape is of the body is an inverted cone of angle 45 degree. Then isn't the question simply to find the integral of that function from p = 0 to p = 1, z = 0 to z = 1 and ∅ = 0 to ∅ = 2∏?

Since:

x = p cos∅
y = p sin∅
z = z


x²+y² ≤ z², 0 ≤ z ≤ 1

p² ≤ z²

p ≤ z

 

[SammyS]

Homework Statement

The problem is attached in the picture.

The Attempt at a Solution

My question is, why can't the limits of ∫(dp) be from 0 to 1?

The shape is of the body is an inverted cone of angle 45 degree. Then isn't the question simply to find the integral of that function from p = 0 to p = 1, z = 0 to z = 1 and ∅ = 0 to ∅ = 2∏?

Doing what you suggest would be integrating over a right circular cylinder of radius 1 and height of 1.