Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

Solution

$straight V space equals space straight x cubed$
$Now space space space space space space space space space dV space equals space open parentheses dV over dx close parentheses increment straight x space equals space 3 straight x squared increment straight x space space space space space space space space space space space space space space space space space space space space space space equals space 3 straight x squared left parenthesis 0.01 space straight x right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space 1 percent sign space of space straight x space is space 0.01 space straight x close square brackets$
$equals space 0.03 space straight x cubed straight m cubed$
$therefore space space space space approximate space change space in space volume space space equals space 0.03 space straight x cubed straight m cubed.$

For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction