# Help w/ double integration to solve common volume of two intersecting cylinders

## Main Question or Discussion Point

Hi I am taking MV calc and a paticular question in the double integrals chapter asks to find the volume bounded by x^2 + y^2 = r^2 and y^2 +
z^2 = r^2. I already know what the shape looks like (Steinmatic solid) and also know the answer can be achieved using single integration as well, but here I am having difficulty visualizing the integrand for a D. Integral--- the limits of integration will definetely involve constants of r. What would be your suggestion for setting up the integral? The shape is identical on all sides and symmetical--- could there be a way to solve one region and multiply the answer to get the volume, or something along those lines?

matt grime
Homework Helper
The integrand is 1. What the limits are is more interesting. do it in the order, what dx then dy then dz

x from 0 to sqrt(r^2-y^2),

y from 0 to sqrt(r^2-z^2)

z from 0 to r

That sound right to everyone else?

Multiplying by 8 makes total sense!!! Thanks i ended up getting (16/3)*r^3 exactly what it should be! Thanks.

how would u write it if it were a double integral not triple?

Redbelly98
Staff Emeritus