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Need solution for RD Sharma maths class 12 chapter Derivative as a Rate Measure exercise 12.1 question 3

Answers (1)

Answer: 1cm


Here we have to differentiate volume of sphere with respect to surface area of sphere

V\! olume\; o\! f\; spher\! e, V=\frac{4}{3}\pi r^{2}

\therefore S\! ur\! f\! ace\; area\; o\! f\; spher\! e, A=4\pi r^{2}


Radius of sphere, r=2cm


Here we have,

Radius, r=2cm

Area, A=4\pi r^{2}

Let’s differentiate it with respect to area (A)

\Rightarrow \frac{d(A)}{dA}=4(2)\pi r\frac{dr}{dA}                                    \left[\because \frac{d\left(x^{n}\right)}{d x}=n x^{n-1}\right]

\Rightarrow 1=8\pi r\frac{dr}{dA}

\therefore \frac{dr}{dA}=\frac{1}{8\pi r}\; \; \; \; \; \; \; \; \; \; \; ......(i)

V\! olume, V=\frac{4}{3}\pi r^{3}

Let’s differentiate with respect to Area (A)

\Rightarrow \frac{d V}{d A}=4\pi r^{2}\frac{dr}{d A}

\Rightarrow \frac{d V}{d A}=\frac{4\pi r^{2}}{8\pi r}                                                        {From the Equation (i)}

\therefore \frac{d V}{d A}=\frac{r}{2}

To putting value of r=2cm

                                \therefore \frac{d V}{d A}=1cm


We cannot put Area directly in formula of volume,

V=\frac{4}{3}\pi r^{2}

S\! o, we\; can\; not\; write,V=\frac{A.r}{3}

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Gurleen Kaur

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