# Math Help - Double integration

1. ## Double integration

Use double integration to find the volume of the solid that is common to the cylinders x^2 + y^2 =25 and x^2 + z^2 = 25.

Thank you very much.

2. You could find the volume of one octant and then multiply by 8.

$8\int_{0}^{5}\int_{0}^{\sqrt{25-x^{2}}}\sqrt{25-x^{2}}dydx$

= $8\int_{0}^{5}(25-x^{2})dx$

3. Hi galactus,

thank you very much for your reply. Why multiple by 8? Could you please explain to me? Thanks.

4. Originally Posted by kittycat
Hi galactus,

thank you very much for your reply. Why multiple by 8? Could you please explain to me? Thanks.
He used symmetry.

The shape was equally divided into the 8 octants. He chose only 1 octant and multiplied it by 8.

5. Originally Posted by ThePerfectHacker
He used symmetry.

The shape was equally divided into the 8 octants. He chose only 1 octant and multiplied it by 8.
Yes. See the graph below.