The diagonal of a square is changing at the rate of 0.5 ~cm / sec . Then the rate of change of area, when the area is 400 ~cm ² , is equal to

Step-by-step solution

Diagonal D = 2 a Differentiating w.r.t. t: dD dt = 2 da at or da dt = 1 2 da dt = 1 2 0.5 ~cm / s Let Area is denoted by A d A dt =2 a da dt when area A is 400 ~cm ² then a =20 d A dt =2 20 0.5 2 =10 2 ~cm ² / sec