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Thread: Area word problem

  1. #1
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    Area word problem

    when mineral deposits formed a coating 1 mm thick on the inside of a pipe, the area through which fluid can flow was reduced by 20%. Find the original inside diameter.
    area of circle = pi(r^2) diameter 2r

    please help me my math teacher gives so many different word problems... please help me with this problem :'(
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lightstevoo View Post
    when mineral deposits formed a coating 1 mm thick on the inside of a pipe, the area through which fluid can flow was reduced by 20%. Find the original inside diameter.
    area of circle = pi(r^2) diameter 2r

    please help me my math teacher gives so many different word problems... please help me with this problem :'(
    we just need to find $\displaystyle r$, then multiply it by 2 to find the diameter $\displaystyle D = 2r$.

    The original area is $\displaystyle A_1 = \pi r^2$

    When the radius is decreased by 1mm, the area is $\displaystyle A_2 = \pi (r - 1)^2$

    But that is 20% of $\displaystyle A_1$. Thus we have

    $\displaystyle A_2 = 0.2A_1$

    $\displaystyle \Rightarrow \pi (r - 1)^2 = 0.2 \pi r^2$

    Now solve for $\displaystyle r$ so you can answer the problem
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