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Provide solution for RD Sharma maths class 12 chapter Derivative as a Rate Measure exercise 12.1 question 6

Answers (1)


10\pi cm^{2}/cm


Here we have to differentiate Area of circle (A) with respect to its radius (r)

Area of circle, A=\pi r^{2}


Radius of circle, r=5cm


Here we have,

r = Radius of circle = 5cm

Area of circle, A=\pi r^{2}

Let’s differentiate A  with respect to radius

\therefore \frac{d A}{d r}=\frac{d}{d r}\left(\pi r^{2}\right)

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

Put, r=5cm

                            \therefore \frac{d A}{d r}=10\pi cm^{2}/cm


Here unit of rate is cm2/cm  we can’t write unit cm because it shows rate means

Area (A) varying with respect to radius (r)

Posted by

Gurleen Kaur

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