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KCET2018MathematicsApplication of Derivatives

Approximate change in the volume ( V ) of a cube of side ( x ) metres caused by increasing the side by ( 3 % ) is

Options

  1. A( 0.09 x³ m³ )
  2. B( 0.03 x³ m³ )
  3. C( 0.06 x³ m³ )
  4. D( 0.04 x³ m³ )

Correct answer

A. ( 0.09 x³ m³ )

Step-by-step solution

Given sides of a cube ( x ~m ). We know that, volume of cube is given by, ( V=x³ ) and ( d x x 100=3 ) Now, ( d V=3 x² d x ) ( d V=3 x² d x ) ( =3 x³ d x x =3 x³ 3 100 ) ( =0.09 x³ )

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