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Math Help - Cone Problem

  1. #1
    Junior Member BobBali's Avatar
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    Cone Problem

    Hi All,

    The problem below shows a sector of a circle on the right hand side and when it is folded it makes the cone on the left. Find the arc length.

    I started of by finding the slant height or radius:

    \sqrt{10^2 + 6^2} = 11.7

    To find arc length i have the formula:
    \frac{\theta}{360} \times 2\pi r

    But, How do i find the angle in the unfolded sector?

    I tried finding the the angle of the top part of the cone using:
    tan\theta = \frac{6}{10} = 31 \times 2 = 62

    Then, 360 - 62 = 329 But, this input into the arc-length formula is not the
    right answer.
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  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
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    Germany
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    Re: Cone Problem

    Quote Originally Posted by BobBali View Post
    Hi All,

    The problem below shows a sector of a circle on the right hand side and when it is folded it makes the cone on the left. Find the arc length.

    I started of by finding the slant height or radius:

    \sqrt{10^2 + 6^2} = 11.7

    To find arc length i have the formula:
    \frac{\theta}{360} \times 2\pi r

    But, How do i find the angle in the unfolded sector?

    I tried finding the the angle of the top part of the cone using:
    tan\theta = \frac{6}{10} = 31 \times 2 = 62

    Then, 360 - 62 = 329 But, this input into the arc-length formula is not the
    right answer.
    Obviously the arc length equals the circumference of the base area:

    c_{base} = 2 \cdot \pi \cdot 6

    If (and only if) you want to to know the central angle of the sector you have to determine the length of s using Pythagorean theorem. Then use the proportion:

    \frac{\theta}{360^\circ}=\frac{2 \cdot \pi \cdot 6}{2 \cdot \pi \cdot s}

    Solve for \theta.
    Attached Thumbnails Attached Thumbnails Cone Problem-keglaussektor.png  
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