Question

The radius of a circle varies with time is given as r = t^2+2t+1. The rate of change of area of the circle at t = 1 will be-
(a) 32pi m/s
(b) 16pi m/s
(c) 24pi m/s
(d) 8pi m/s

Answer 1

Answer:

32π m/s

Explanation:

The radius of a circle varies with time is given as r = t^2+2t+1. The rate of change of area of the circle at t = 1 will be

Area of circle = π R²

dA/dt  =  2 π R dR/dt

=> dA/dt = 2 π (t² + 2t + 1)d(t² + 2t + 1)/dt

=> dA/dt = 2 π(t² + 2t + 1)( 2t + 2)

at t = 1

=>  dA/dt = 2 π(1² + 1*2 + 1)( 2*1 + 2)

=> dA/dt = 2 π(1 + 2 + 1)( 2 + 2)

=> dA/dt = 2 π(4)( 4)

=> dA/dt = 32 π

The rate of change of area of the circle at t = 1 will be 32pi m/s

Answer 2

Answer:

Option a is the right answer

pls refer to the attachments (2 pics) for the explanation..

Hope it helps :)