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  • Please solve RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise very short answer question 5 maths textbook solution

Please solve RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise very short answer question 5 maths textbook solution

Answers (1)

Answer: 3a

Hint:

Here we use basic formula of cube,        

                V=x^{3}

Given:

The percentage error in the edge of cube is a

Solution:

Let x be the side and Vbe the volume of the cube

V=x^{3}

We have,

\frac{\Delta x}{x} \times 100=a           

\frac{d V}{d x}=3 x^{2}          

\frac{\Delta V}{V}=\frac{3 x^{2}}{V} \times \Delta x         

\frac{\Delta V}{V}=\frac{3 x^{2}}{x^{3}} \times \frac{\Delta x}{100}            

\frac{\Delta V}{V} \times 100=3 a    \left[\because \frac{d\left(x^{n}\right)}{d x}=n x^{n-1}\right]

Hence, the percentage error in volume of cube is  3a

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