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Application Of Derivatives

Question
CBSEENMA12035623
Wired Faculty App

The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is

  • 0.06 x3 m3

  • 0.6 x3 m3
  • 0.09 x3 m3
  • 0.9 x3 m3

Solution

C.

0.09 x3 m3

Let V be volume of cube of side x metre.
therefore space space space space space space space space space space space space space space space straight V space equals space straight x cubed Now comma space space space space space space space space dV space equals space open parentheses dV over dx close parentheses increment straight x space equals space left parenthesis 3 straight x squared right parenthesis space increment straight x space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis 3 straight x squared right parenthesis thin space. space left parenthesis 0.03 space straight x right parenthesis space space space space space space space space space space space space space space space space open square brackets because space space space 3 percent sign space of space straight x space equals space 0.03 space straight x close square brackets space space space space space space space space space space space space space space space space space dV space equals space 0.09 space straight x cubed straight m cubed therefore space space space approximate space change space in space voume space space equals space 0.09 space straight x cubed space straight m cubed therefore space space space space left parenthesis straight C right parenthesis space is space correct space answer.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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