# Thread: Mass of Ice Cream Cone using Triple Integrals

1. ## Mass of Ice Cream Cone using Triple Integrals

Hey!
I'm trying to find the mass of an ice cream cone made by 2 surfaces.
The first is a sphere with radius 5 at the origin.
The second is a cone centered around the positive z-axis emanating from the origin. The two intersect to make a circle of radius 3.
The density is density= z mg/cm^3 (all dimensions were given in cm)

Mainly I don't understand how to set the limits for the integration in terms of spherical.
All help is greatly appreciated! Really stumped on where to begin.

2. ## Re: Mass of Ice Cream Cone using Triple Integrals

You're integrating z in a triple integral very like the first example here, Pauls Online Notes : Calculus III - Triple Integrals in Spherical Coordinates.

So you'll have, int_0^(arcsin(3/5)) int_0^(2*pi) int_0^5 1/2 r^3 sin(2p) dr dt dp - Wolfram|Alpha

And, just in case a picture helps for working through the triple from the inside out...

__________________________________________________ ___________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!

3. ## Re: Mass of Ice Cream Cone using Triple Integrals

If you look at the cone, it needs to have the equation $z = \frac{4}{3}\sqrt{x^2+y^2}$ in order for its intersection with the sphere to be a circle with radius 3.