question_answer

If the radius of a circle is increased from 5 cm to 5.1 cm. Find the approximate increase in area.

Answer:

Area of a circle of radius r is given by, \[A=\pi {{r}^{2}}\] Then, r = 5, \[r+\Delta r=5.1,\Delta r=0.1\] \[\therefore \] \[\Delta \,A=\frac{dA}{dr}\Delta r=2\pi r\times 0.1=2\pi \times 5\times 0.1=\pi \,c{{m}^{2}}\]