Question

a stone is dropped into white lake of wheels moves in Circles at the speed of 5 cm per second at the instant when the radius of circular wire is 8 cm how fast is the enclosed area increase

Answer 1

hope this answers will help you

Answer 2

${ \huge{\boxed{\tt {\color{red}{Answer}}}}}$

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

We know that the area of a circle with radius “r” is given by A = πr2.

Hence, the rate of change of area “A’ with respect to the time “t” is given by:

dA/dt = (d/dt) πr2

By using the chain rule, we get:

(d/dr)(πr2). (dr/dt) = 2πr.(dr/dt)

It is given that, dr/dt = 4 cm/sec

Therefore, when r = 10 cm,

dA/dt = 2π. (10). (4)

dA.dt = 80 π

Hence,

when r = 10 cm, the enclosing area is increasing at a rate of 80π cm2/sec

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

Hope It's Helpful....:)