Question

The rate of change of the area of a circular disc with respect to its circumference when the radius is 3 cm, is.

• A. 1 cm
• B. 4 cm
• C. 3 cm
• D. 2 cm

Answer 1

The correct option is C 3 cm

Let radius of the disc be $r$
Thus it's area $A=\pi r^2$ and circumference $S=2\pi r$
Now $\frac{dA}{dr}=2\pi r,\frac{dS}{dr}=2\pi$ $\therefore \frac{dA}{dS}=r$
Hence rate of change of area of disc w.r.t circumference at $r=3$ cm is $=3$ cm.