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Provide solution for RD Sharma maths class 12 chapter 13 Differentials Errors and Approximations exercise  multiple choice question 2

Answers (1)


Answer:  A)  2a%

Hint: Here we all know the formula about surface area(A) of cube

                A=6 a^{2}

Given: Percentage error in measuring side=a%


Here x be the side of cube

\begin{aligned} &\frac{\Delta x}{x} \times 100=a \\\\ &\text { So } \quad \Delta x=\frac{a x}{100} \end{aligned}

and  y  be the surface area

\begin{aligned} &\text { So, }\\ &\begin{aligned} &y=6 x^{2} \\\\ &\frac{d y}{d x}=\Delta y=12 x \times \Delta x \end{aligned}\\\\ &=12 x \times \frac{a x}{100} \end{aligned}

So,%  error in surface area      \begin{aligned} &=\frac{\Delta y}{\mathrm{y}}=\frac{\frac{12 a}{100} \times x^{2}}{6 x^{2}} \end{aligned}

                                                       =2 a \%

So, option (A) 2a% is correct.

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