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# Solution for If There is an Error of A% in Measuring the Edge of a Cube, Then Percentage Error in Its Surface is (A) 2a% (B) a 2 %(C) 3a% (D) None of These - CBSE (Commerce) Class 12 - Mathematics

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#### Question

If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is
(a) 2a%

(b)$\frac{a}{2} \%$

(c) 3a%

(d) none of these

#### Solution

(a) 2a%
Let x be the side of the cube and y be its surface area.

$\frac{∆ x}{x} \times 100 = a$

$\text { Also }, y = 6 x^2$

$\Rightarrow \frac{dy}{dx} = 12x$

$\Rightarrow \frac{∆ y}{y} = \frac{12x}{y} \times dx = \frac{2}{x} \times \frac{ax}{100}$

$\Rightarrow \frac{∆ y}{y} \times 100 = 2a$

$\text { Hence, the error in the surface area is} 2a % .$

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Solution If There is an Error of A% in Measuring the Edge of a Cube, Then Percentage Error in Its Surface is (A) 2a% (B) a 2 %(C) 3a% (D) None of These Concept: Approximations.
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