Suppose two cylindrical tubes with the same diameter intersect at right angles. If the diameter of each tube is 6 cm, find the volume of the common part between the tubes. Use the prismatoid formula.

Question

anonymous · Answer

I found no reference to this prismatoid formula you speak of online,  but you could do this with a double integral:$$8 \int\limits_0^3\int\limits_{-x}^x \sqrt{9-x^2} dydx$$

anonymous · Answer

The two integrals give the volume of this shaded eighth of the volume:|dw:1393540988381:dw|
Sorry if it's hard to make sense of; I did my best but I'm not a good draughtsman.