Application of Derivatives — Class 12 Maths Solution

ncert exercise SA NCERT Ex. 6.4, Q.5,Page 216
Question

Find the approximate change in the surface area of a cube of side $x$ metres caused by decreasing the side by $1\%$.

Step-by-step Solution

Surface area $S$ of given cube , $S = 6{x^2}$
$\Rightarrow \cfrac{{dS}}{{dx}} = 12x$

Hence, $\Delta S \approx 12x\Delta x = 12x\left( { - \cfrac{x}{{100}}} \right)$

$= - \cfrac{{12{x^2}}}{{100}}\,\,\,{m^2}$

Therefore the change in surface area$= 0.12{x^2}{m^2}$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Application of Derivatives. Curated by Sachin Sharma. Free for all students.