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# Applications of the Integral Practice Test (page 2)

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By — McGraw-Hill Professional
Updated on Aug 31, 2011

1. At position x in the base circle, the y -coordinate is . Therefore the half-disk slice has radius and area π (1 − x 2 )/2. The volume of the solid is then

2.  We calculate the volume of half the solid, and then double the answer. For , at position x in the base square, the y -coordinate is . Thus the disk slice has radius and area . Thus the volume of the solid is

3.

4.

5. The depth of points in the window ranges from 6 to 10 feet. At depth x in this range, the window has chord of length . Thus the total pressure on the lower half of the window is

6. At depth x , the corresponding subtriangle has side-length . Therefore the total pressure on one end of the pool is

7. Let t  = 0 be the moment when the climb begins. The weight of the sack at time t is then 100 − t pounds. Then the work performed during the climb is

Thus

8. The work performed is

9.

10.

11.

12. We do (a) and (b).

13. We do (a) and (b)

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