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  • Please solve RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 7 maths textbook solution

Please solve RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 7 maths textbook solution

Answers (1)

Answer:  (c) 80000 \pi \; m m^{3}

Hint:

Here we use the formula about volume of sphere,

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

Given:

        r=100 \mathrm{~mm} shrinks to  r=98 \mathrm{~mm}

Solution:

Let x be the radius of the sphere,x=100

\begin{array}{ll} \therefore & x+\Delta x=98 \\\\ \therefore & \quad \Delta x=98-100=-2 \end{array}

Let y be the volume of the sphere

        y=\frac{4}{3} \pi x^{3}

Let’s differentiate,

\begin{aligned} &\frac{d y}{d x}=4 \pi x^{2} \\\\ &\left(\frac{d y}{d x}\right)_{x=100}=4 \pi(10000)=40000 \pi \end{aligned}

\begin{aligned} \Delta y &=d y=\frac{d y}{d x} \times \Delta x \\\\ &=40000 \pi \times(-2) \\\\ &=-80000 \pi \end{aligned}

Hence, the decrease in volume of sphere is 80000 \pi \; m m^{3}.

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