MathematicsA sphere of diameter 15.6 cm is melted and cast into a right circular cone of height 31.2 cm. The diameter of the base of the cone is ____.

A sphere of diameter 15.6 cm is melted and cast into a right circular cone of height 31.2 cm. The diameter of the base of the cone is ____.


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    Solution:

    It is given that the diameter of the sphere is 15.6 cm.
    The radius of the sphere is 15.6 2 =7.8 cm   .
    It is given that the height of the cone is 31.2cm.
    Let the radius of the cone is r cm.
    We know that,
    The volume of the sphere is where r is the radius of the sphere.
    The volume of the corner is where r is the radius of the cylinder and h is the height of the cone.
    According to the question, we get:
    4 3 π× r 3 = 1 3 π× r 2 ×h 4 3 π× 7.8 3 = 1 3 ×π× r 2 ×31.2 r 2 = 4 3 π× 7.8 3 1 3 ×π×31.2 r 2 = 4×474.552 31.2   Further, simplify the radius as,
    The diameter of the wire will be:
     Therefore, the diameter of the base of the cone is 15.6 cm.
     
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