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  4. If the side of a cube is increased by 5%, then the surface area of a cube is increased by

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Q. If the side of a cube is increased by 5%, then the surface area of a cube is increased by

KCETKCET 2020

Solution:

Let one side of the cube be $x$ and surface area be $A$
So, $dx =5 \%=5 x / 100$
Then, $A=(6 x)^{2}$
$\Rightarrow dA / dx =12 x$
$\Rightarrow d A =(12 x ) d x$
$\Rightarrow dA =(12 x )(5 x / 100)$
$\Rightarrow d A =10 A / 100$
$\Rightarrow dA =10 \%$