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16 September, 07:29

The vertical height of a right circular conical tent is 4m and the volume of space inside it is 968/7 cubic metre. Find the canvas required to make the tent.

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  1. 16 September, 07:49
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    The equation for the volume of a conical tent is

    v = 1/3 * height * area of the base

    = 1/3 * hπr²

    where v - volume

    h - height of the conical tent

    r - radius of base circle

    area of the base = 3v/h

    πr² = 3 * 968/7 m³ / 4 m

    r² = 3 * 968 * 7 / (7 * 22 * 4)

    = 33

    r = 5.74 m

    area of the curved surface = πrl

    where l is the slant height

    l² = r² + h²

    = 5.74² + 4²

    = 33 + 16

    = 49 m

    l = 7 m

    then the area of the curved surface is;

    area = πrl

    = (22/7) * 5.74 * 7

    = 126.28 m²

    the canvas should have area 126.28 m² to cover the tent
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