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Math Help - Height of cone

  1. #1
    Member helloying's Avatar
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    Height of cone

    pls teach me how to start amd solve part (A). thank you very much
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  2. #2
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    Quote Originally Posted by helloying View Post
    pls teach me how to start amd solve part (A). thank you very much
    OQ is the slant height of the cone.

    The formula for the Total Surface Area of a cone is

    \textrm{TSA} = \pi r^2 + \pi r s

    where r is the radius and s is the slant height.

    Note that \pi r^2 is the area of the circular base, so \pi r s is the curved area.


    Since you're told that the curved surface has area 252 \pi \,\textrm{cm}^2 and the radius r = 14\,\textrm{cm}, we have

    252 \pi \,\textrm{cm}^2 = 14\pi\,\textrm{cm}\cdot s

    s = \frac{252\pi\,\textrm{cm}^2}{14\pi\,\textrm{cm}}

    s = 18\,\textrm{cm}.


    You can find the height OP using the Pythagorean Theorem.
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