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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.

\[\frac{∆ x}{x} \times 100 = a\]

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

\[ \Rightarrow \frac{dy}{dx} = 12x\]

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

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

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

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 14: Differentials, Errors and Approximations
Q: 2 | Page no. 13

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Solution for 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) a 2 %(C) 3a% (D) None of These concept: Approximations. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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