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Solution for Find the Percentage Error in Calculating the Surface Area of a Cubical Box If an Error of 1% is Made in Measuring the Lengths of Edges of the Cube ? - CBSE (Science) Class 12 - Mathematics

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Question

Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of edges of the cube ?

Solution

Let x be the edge of the cube and y be the surface area.

\[y = x^2 \]

\[\text { Let } ∆ x \text { be the error in x and } ∆ y \text { be the corresponding error in } y . \]

\[\text { We have }\]

\[\frac{∆ x}{x} \times 100 = 1\]

\[ \Rightarrow 2x = \frac{x}{100} \left[ \text { Let } dx = ∆ x \right]\]

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

\[ \Rightarrow \frac{dy}{dx} = 2x\]

\[ \therefore ∆ y = \frac{dy}{dx} \times ∆ x = 2x \times \frac{x}{100}\]

\[ \Rightarrow ∆ y = 2\frac{x^2}{100}\]

\[ \Rightarrow ∆ y = 2\frac{y}{100}\]

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

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

Hence, the percentage error in calculating the surface area is 2.

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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: 4 | Page no. 9

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Solution for question: Find the Percentage Error in Calculating the Surface Area of a Cubical Box If an Error of 1% is Made in Measuring the Lengths of Edges of the Cube ? concept: Approximations. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
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