The edge of a cube is equal to the radius of a sphere. If the edge and the radius increase at the same rate, then the ratio of the increases in surface areas of the cube and sphere is 

 The edge of a cube is equal to the radius of a sphere. If the edge and the radius increase at the same rate, then the ratio of the increases in surface areas of the cube and sphere is 

  1. A

    2π: 3

  2. B

    3:2π

  3. C

    6:π

  4. D

    none of these 

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    Solution:

    Let the length of an edge of the cube be x units. Let S1and S2 be the surf ace areas of the cube and sphere respectively. Then, 

    S1=6x2  and S2=4πx2

     dS1dt=12xdxdt  and S2=8πxdxdtds1dtdS2dt=32π

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