Find the approximate change in the volume V of a cube of side v meters caused by increasing the side by 2%.

Solution

$straight V space equals space straight x cubed$
$Now space dV space equals space open parentheses dV over dx close parentheses increment straight x space equals space left parenthesis 3 straight x squared right parenthesis space increment straight x space space space space space space space equals left parenthesis 3 straight x squared right parenthesis space left parenthesis 0.02 space straight x right parenthesis space space space space space space space space equals space 0.06 space straight x cubed straight m cubed space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis as space 2 percent sign space of space straight x space is space 0.02 space straight x right parenthesis therefore space space space the space approximate space change space in space volume space is space 0.06 straight x cubed straight m cubed.$

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Application Of Derivatives

Find the approximate change in the volume V of a cube of side v meters caused by increasing the side by 2%.

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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