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

[Theelectricchild]

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 definitely 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?

Thanks for your help.

 

[matt grime]

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

multiply that answer by 8

That sound right to everyone else?

 

[Theelectricchild]

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

 

[kmelon]

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

 

[Redbelly98]

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