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15 August, 19:14

The base of a right circular cone has a radius of 4 inches and a slant height of 9 inches. If the radius and the slant height are multiplied by 6, by what factor is the surface area multiplied? A. 6 B. 36 C. 24 D. 54

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  1. 15 August, 19:41
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    Correct option: B - > 36

    Step-by-step explanation:

    The surface area of a circular cone is given by the formula:

    Surface area = pi * radius * (radius + slant height)

    If the inicial radius is 4 in and the slant height is 9 in, we have:

    Surface area = pi * 4 * (4 + 9) = 52pi in2

    The radius and the slant height are multiplied by 6, so we have:

    radius = 6 * 4 = 24 in

    slant height = 6 * 9 = 54 in

    So the new surface area is:

    New surface area = pi * 24 * (24 + 54) = 1872pi in2

    The factor of the surface areas is:

    New surface area / Surface area = 1872pi / 52pi = 36

    Correct option: B
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