Question

A circular metal plate expands under heating so that its radius increases by 2%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.

Answer 1

Let the radius of the plate 10 cm.

Radius increases by 2% by heating

∴ After increment = 2/100 x 10 = 0.2

Change in radius dr = 0.2

∴ New radius = 10+0.2 = 10.2 cm

Area of circular plate = A = πr²

∴ Change in Area = \(\frac{dA}{dr}\)