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Math Help - Lateral surface area of a cone

  1. #1
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    Lateral surface area of a cone



    I don't have the foggiest clue how to answer this question. Also, I don't have any intuition how to answer this without memorizing formulas. I've googled and found the formula for a lateral surface area of a cone: L = \pi*r*\sqrt{r^2 + h^2}

    Now my test taking skills, I figured I can eliminate choices till I get a 50-50 guess.
    • My thought process knows there is 360 deg in a circle. There are nine - 40deg's in a circle. So that leaves me with B or D.
    • This thought process may be wrong: (And if I was in the test without the formulas in front of me). I know that a cone and a sphere both are curved. I know the surface area of a sphere has a radius squared. So I would presume I would square the 8" to get 64. So I would choose D, here.


    But as I said earlier, I do not have any intuition on how to definitively answer this question. So how about it? Am I on the right track?
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  2. #2
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    Quote Originally Posted by EMyk01 View Post


    I don't have the foggiest clue how to answer this question. Also, I don't have any intuition how to answer this without memorizing formulas. I've googled and found the formula for a lateral surface area of a cone: L = \pi*r*\sqrt{r^2 + h^2}

    Now my test taking skills, I figured I can eliminate choices till I get a 50-50 guess.
    • My thought process knows there is 360 deg in a circle. There are nine - 40deg's in a circle. So that leaves me with B or D.
    • This thought process may be wrong: (And if I was in the test without the formulas in front of me). I know that a cone and a sphere both are curved. I know the surface area of a sphere has a radius squared. So I would presume I would square the 8" to get 64. So I would choose D, here.


    But as I said earlier, I do not have any intuition on how to definitively answer this question. So how about it? Am I on the right track?
    Your guessing skills are excellent

    The lateral surface of a cone is a sector, that means a part of a circle. As you've said correctly you have \dfrac{40}{360} of a circle with a radius of 8''.

    The area of the complete circle is calculated by:

    a_{circle}=\pi r^2

    So in your case

    a_{sector}=\dfrac{40}{360} \cdot \pi \cdot 8^2

    Simplify the RHS and you'll get answer D. (But of course: Guessing is much faster)
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  3. #3
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    And there is the intuition I was missing! It sounds silly, but I never realized that we were working with a section of a circle. :-p Wow, I am glad I understand it now instead of going into this feeling silly. Thanks.

    Quote Originally Posted by earboth View Post
    Your guessing skills are excellent

    The lateral surface of a cone is a sector, that means a part of a circle. As you've said correctly you have \dfrac{40}{360} of a circle with a radius of 8''.

    The area of the complete circle is calculated by:

    a_{circle}=\pi r^2

    So in your case

    a_{sector}=\dfrac{40}{360} \cdot \pi \cdot 8^2

    Simplify the RHS and you'll get answer D. (But of course: Guessing is much faster)
    Follow Math Help Forum on Facebook and Google+

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