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How do you calculate the lateral and surface areas of a cone whose height is 12 in and whose slant height is 15 in.

  • geometry -

    Draw a cross section and you will have a right-angled triangle.
    find the missing side which will be the radius of the base of the cone , r should be 9 in
    You should have formulas for the surface area of a cone.

  • geometry -

    Could you show me the work for this one.
    Thank you

  • geometry -

    r^2 + 12^2 = 15^2
    r^2 = 225-144 = 81
    r = √81 = 9

    The surface area is made up of two parts,
    the base, which is a circle, πr^2 and
    the lateral surface (without the base) which has an area of πrs, where s is the slant height of 15 in

    So total area is
    πr^2 + πrs
    = π(9^2) + π(9)(15)
    = .....

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