Maths-
General
Easy

Question

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. 2 pi blank colon 3  
  2. 3 blank colon 2 pi  
  3. 6 blank colon pi  
  4. None of these  

The correct answer is: 3 blank colon 2 pi


    Let the length of an edge of the cube be x units. Let S subscript 1 end subscript and S subscript 2 end subscript be the surface areas of the cube and sphere respectively. Then,
    S subscript 1 end subscript equals 6 x to the power of 2 end exponent and equals S subscript 2 end subscript equals 4 pi x to the power of 2 end exponent

    rightwards double arrow fraction numerator d S subscript 1 end subscript over denominator d t end fraction equals 12 x fraction numerator d x over denominator d t end fraction and S subscript 2 end subscript equals 8 pi x fraction numerator d x over denominator d t end fraction rightwards double arrow fraction numerator fraction numerator d S subscript 1 end subscript over denominator d t end fraction over denominator fraction numerator d S subscript 2 end subscript over denominator d t end fraction end fraction equals fraction numerator 3 over denominator 2 pi end fraction

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