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Applications of the Integral Practice Test (page 2)

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

Answers

  1. At position x in the base circle, the y -coordinate is SOLUTIONS TO EXERCISES Chapter 8 . Therefore the half-disk slice has radius SOLUTIONS TO EXERCISES Chapter 8 and area π (1 − x 2 )/2. The volume of the solid is then

    SOLUTIONS TO EXERCISES Chapter 8

  2.  We calculate the volume of half the solid, and then double the answer. For SOLUTIONS TO EXERCISES Chapter 8, at position x in the base square, the y -coordinate is SOLUTIONS TO EXERCISES Chapter 8. Thus the disk slice has radius SOLUTIONS TO EXERCISES Chapter 8 and area SOLUTIONS TO EXERCISES Chapter 8. Thus the volume of the solid is

    SOLUTIONS TO EXERCISES Chapter 8

  3.  

    SOLUTIONS TO EXERCISES Chapter 8

  4.  

    SOLUTIONS TO EXERCISES Chapter 8

  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 SOLUTIONS TO EXERCISES Chapter 8 . Thus the total pressure on the lower half of the window is

    SOLUTIONS TO EXERCISES Chapter 8

  6. At depth x , the corresponding subtriangle has side-length SOLUTIONS TO EXERCISES Chapter 8 . Therefore the total pressure on one end of the pool is

    SOLUTIONS TO EXERCISES Chapter 8

  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

    SOLUTIONS TO EXERCISES Chapter 8

    Thus

    SOLUTIONS TO EXERCISES Chapter 8

  8. The work performed is

    SOLUTIONS TO EXERCISES Chapter 8

  9.  

    SOLUTIONS TO EXERCISES Chapter 8

  10.  

    SOLUTIONS TO EXERCISES Chapter 8

  11.  

    SOLUTIONS TO EXERCISES Chapter 8

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

    SOLUTIONS TO EXERCISES Chapter 8

  13. We do (a) and (b)

    SOLUTIONS TO EXERCISES Chapter 8

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