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  • Explain solution RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise very short answer question 4 maths

Explain solution RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise very short answer question 4 maths

Answers (1)

Answer: 3\alpha

Hint:

 

Here we use the basic concept of approximation.

 

Given:

The percentage error in radius of sphere is  \alpha

Solution:

Let Vbe the volume of the sphere

V=\frac{4}{3} \pi r^{3}

let radius r =x

We have,

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

After differentiating,

\begin{aligned} &\frac{d V}{d x}=4 \pi x^{2} \\\\ &\frac{d V}{V}=\frac{4 \pi x^{2}}{V} d x \end{aligned}

\begin{aligned} &\frac{\Delta V}{V}=\frac{4 \pi x^{2}}{\frac{4}{3} \pi x^{3}} \times \frac{x \alpha}{100} \\\\ &\frac{\Delta V}{V} \times 100=3 \alpha \end{aligned}

Hence, the percentage error in volume of sphere is 3\alpha

 

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