Question

ant) THE INTERSECTION OF THREE CYLINDERS The figure shows the solid enclosed by three circular cylinders with the same diameter that inter- right angles. In this project the cylinders have different diameters. we compute its volume and determine how its shape changes if sect at 1. Sketch carefully the solid enclosed by the three cylinders x2 +y2 1, x2+z2 1, and y2 + z2= 1. Indicate the positions of the coordinate axes and label the faces with the equa- tions of the corresponding cylinders. 2. Find the volume of the solid in Problem 1. 3. Use a computer algebra system to draw the edges of the solid. 4. What happens to the solid in Problem 1 if the radius of the first cylinder is different from 1? Illustrate with a hand-drawn sketch or a computer graph. 5. If the first cylinder is x2 + y2 = a2, where a < 1, set up, but do not evaluate, a double inte- gral for the volume of the solid. What if a > 1?

Answer 1

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EXPLANATION:

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