Question

A stone is dropped into a quiet lake and waves move in circles at the speed of 5cm/s. At the instant when the radius of the circular wave is 8cm, how fast is the enclosed area increasing? (Class 12 Physics) (No Spam, Irrelevant answers will be reported)

Answer 1

Explanation:

Aloha !

Area of circle= πr²

A= πr²

Diff w.r.t t

dA/dt = d(πr²)/dt

dA/dt= π d(r²)/dt× dr/dt

dA/dt= π×2r ×dr/dt

dA/dt= 2πr×dr/dt

dA/dt=2πr×5

dA/dt=10πr

dA/dt=10π(8)

dA/dt=80π cm²/sec

Thank you

Answer 2

Answer:

80π cm²/s

Explanation:

given:

rate of change of radius=dr/dt=5 cm/s

to find:

rate of change of area when r=8 cm

we know,

area of circle (A)=πr²

so,rate of change of area=dA/dt

=d(πr²)/dt

=2πr*d(r)/dt

=2πr*5

so,when r=8cm,then rate of change of area=2π*8*5 cm²/s

=80π cm²/s