Find the Surface Area Between Smaller Sphere and Larger Sphere

A large solid sphere is melted and moulded to from identical right circular cones with base radius and height same as the radius of the sphere. One of these cones is melted and moulded to from a smaller solid sphere. Then the ratio of the surface area of the smaller to the ratio of the surface area of the larger sphere is

  1. 1 : 34/3
  2. 1 : 23/2
  3. 1 : 32/3
  4. 1 : 24/3
Manish Listener Asked on 17th July 2015 in Maths.
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  • 1 Answer(s)

    Answer: (4) 1 : 23/4
    Explanation:-
    Let be the radius of the original sphere is R and the number of the identical cones are N.
    Formula
    The area of a sphere =  4 x pai x R3/3
    Therefore, 4 x pai x R3/3 = N x (pai x R2 x R/3)
    N = 4
    The volume of smaller sphere = pie x R3/3
    The radius of smaller sphere = (R3/4)1/3 = R/2/2/3
    The ratio of area of smaller sphere and area of larger sphere = 1 : 22/3
    Hence, the answer is (4) 1 : 23/4

    Anurag Mishra Professor Answered on 17th July 2015.
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