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explain solution rd sharma class 12 chapter 12 derivatives as a rate measure exercise fill in the blanks question 4 maths

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Answer: 1\; cm^{^{3}}/cm^{2}

Hint: Here, we use the volume of surface area of a cone V=\frac{4}{3}\pi r^{3}

Given: Radius is 2 cm

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

      \Rightarrow \frac{dV}{dr}=3\times \frac{4}{3}\pi r^{2}

                S=4\pi r^{2}

             \frac{dS}{dr}=2\times 4\pi r

                    =8\pi r

            \frac{dV}{dS}=\frac{dV}{dr}\times \frac{dr}{dS}

       => \frac{r}{2}=1\; at\; r=2

So,1\; cm^{^{3}}/cm^{2} is the answer.                    

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