Question:
If the side of a cube is increased by 5%, then the surface area of a cube is increased by
If the side of a cube is increased by 5%, then the surface area of a cube is increased by
Updated On: May 19, 2024
- 0.1
- 0.6
- 0.06
- 0.2
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The Correct Option is A
Solution and Explanation
Let one side of the cube be $x$ and surface area be $A$
So, $dx =5 \%=5 x / 100$
Then, $A=(6 x)^{2}$
$\Rightarrow dA / dx =12 x$
$\Rightarrow d A =(12 x ) d x$
$\Rightarrow dA =(12 x )(5 x / 100)$
$\Rightarrow d A =10 A / 100$
$\Rightarrow dA =10 \%$
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Concepts Used:
Continuity & Differentiability
Definition of Differentiability
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Definition of Continuity
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.