How do you setup in Cartesian form enclosed by the cone z=sqr(x^2+y^2) between the planes z=a and z=b?

Question

where 0 Any ideas?

In dzdydz.

Find volume.

Answer 1

♣ do u want the volume, genius kid? Don’t be mysterious!

Answer 2

The volume V, of a cone with radius r and height h is:

V = πr²h/3

For the cone z = √(x² + y²)
r = h

V = πr³/3

Take the difference between the volume of the cone with height b and height a.

V = πb³/3 - πa³/3 = (π/3)(b³ - a³)

The volume in the first octant is 1/4th of that.

V = (1/4)(π/3)(b³ - a³) = (π/12)(b³ - a³)