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Integration for Volume Given Cross Sections

  1. Apr 11, 2009 #1
    1. The problem statement, all variables and given/known data

    The roof and walls of a storage building are built in the shape modeled by the curve y(x) = 20 - [tex]\frac{x^6}{3,200,000}[/tex]. Each cross section cut perpendicular to the x-axis is a rectangle with a base of 50 feet and a height of y feet.

    In cubic feet the volume of the building is approximately:

    A) 686
    B) 2,000
    C) 17,100
    D) 34,300
    E) 50,000

    2. Relevant equations

    Area = (50)(y(x)) = 50 ( 20 - [tex]\frac{x^6}{3,200,000}[/tex] )

    3. The attempt at a solution

    Given the equation above, I reasoned that the area is the base (the 50 feet) multiplied by the function y(x). I carried the following integration:

    V = [tex]\int^{0}_{20}[/tex] 50 * ( 20 - [tex]\frac{x^6}{3,200,000}[/tex] )

    I get an answer of 17142.86. Is this correct? It's a little off from the problem.
     
  2. jcsd
  3. Apr 11, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    Sure it's right. If you look at the answers they are described as 'approximate' and appear to all be rounded to three significant figures. If you round your answer it certainly matches C).
     
  4. Apr 11, 2009 #3
    Thank you!
     
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