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Math Help - word problem help

  1. #1
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    word problem help

    This problem has me stumped!
    A stone dropped into a pond creates a circular ripple whose radius expands at the rate of 1.5 ft/sec. Assuming the initial radius of the circle is 0, find the number of square feet enclosed by the ripple after one minute.

    Now, I know I have to use (pi)r^2. I'm just not sure where the 1.5 feet and 60 seconds would fit in.
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  2. #2
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    Time 0 sec: pi(0 in)^2 = 0 in^2
    Time 1 sec: pi(1.5 in)^2 = 2.25 pi in^2
    Time 2 sec: pi(2*1.5 in)^2 = 9 pi in^2
    Time 3 sec: pi(3*1.5 in)^2 = 20.25 pi in^2
    ...
    Time 60 sec: pi(60*1.5 in)^2 = ???

    Are you seeing it?

    One more thing. This is in in^2. You must convert to ft^2. Do you know how to do that? It is NOT simply dividing by 12.
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    Time 0 sec: pi(0 in)^2 = 0 in^2
    Time 1 sec: pi(1.5 in)^2 = 2.25 pi in^2
    Time 2 sec: pi(2*1.5 in)^2 = 9 pi in^2
    Time 3 sec: pi(3*1.5 in)^2 = 20.25 pi in^2
    ...
    Time 60 sec: pi(60*1.5 in)^2 = ???

    Are you seeing it?

    One more thing. This is in in^2. You must convert to ft^2. Do you know how to do that? It is NOT simply dividing by 12.
    How would I be able to convert to ft^2? I understand at 60 seconds it would be 90 pi in^2. Would I have to square to 8100?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by lemon301 View Post
    How would I be able to convert to ft^2? I understand at 60 seconds it would be 90 pi in^2. Would I have to square to 8100?
    Factor-label method:
    \frac{1~in^2}{1} \cdot \left ( \frac{1~ft}{12~in} \right )^2
    gives you the conversion factor.

    -Dan
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  5. #5
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    Quote Originally Posted by topsquark View Post
    Factor-label method:
    \frac{1~in^2}{1} \cdot \left ( \frac{1~ft}{12~in} \right )^2
    gives you the conversion factor.

    -Dan
    So do I have to divide 90 by 12? I understand the inches will cancel out but the 12 is throwing me off.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by lemon301 View Post
    So do I have to divide 90 by 12? I understand the inches will cancel out but the 12 is throwing me off.
    Look at that little 2 above the second factor. You have inches times inches, so you need to divide by two factors:
    \frac{1~in^2}{1} \cdot \left ( \frac{1~ft}{12~in} \right )^2 = \frac{1~in^2}{1} \cdot \left ( \frac{1~ft}{12~in} \right ) \cdot \left ( \frac{1~ft}{12~in} \right )

    -Dan
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