Maths-
General
Easy

Question

A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is

  1. 12000 blank pi blank m m to the power of 3 end exponent  
  2. 800 blank pi blank m m to the power of 3 end exponent  
  3. 80000 blank pi blank m m to the power of 3 end exponent  
  4. 120 blank pi blank m m to the power of 3 end exponent  

The correct answer is: 80000 blank pi blank m m to the power of 3 end exponent


    Let x be the radius and V be the volume of the sphere. Then, V equals fraction numerator 4 over denominator 3 end fraction pi x to the power of 3 end exponent
    therefore fraction numerator d V over denominator d x end fraction equals 4 pi x to the power of 2 end exponent

    We have, x equals 100 and x plus increment x equals 98

    therefore increment x equals negative 2

    Now, increment V equals fraction numerator d V over denominator d x end fraction increment x

    rightwards double arrow increment V equals 4 pi cross times 100 to the power of 2 end exponent cross times negative 2 blank open square brackets because open parentheses fraction numerator d V over denominator d x end fraction close parentheses subscript x equals 100 end subscript equals 4 pi cross times 100 to the power of 2 end exponent close square brackets

    rightwards double arrow increment V equals negative 80000 pi

    Hence, decrease in volume is 80000 pi blank m m to the power of 3 end exponent

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