A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed are a increasing?
It is given that when a stone is dropped into a quiet lake, the waves moved in circles at a speed of 5 cm/s .
Let the radius of the circle be r cm .
The formula for the area of circle with radius r is given by,
A = π r 2
Differentiate area A with respect to t,
d A d t = d ( π r 2 ) d t = 2 π r d r d t
As it is given that d r d t = 5 . Therefore,
d A d t = 2 π r ( 5 ) = 10 π r
The radius of circular wave is 8 cm. Therefore,
d A d t = 10 π ( 8 ) = 80 π cm 2 /s
Thus, the area is increasing at rate a of 80 π cm 2 / s .
It is given that when a stone is dropped into a quiet lake, the waves moved in circles at a speed of
Let the radius of the circle be
The formula for the area of circle with radius
Differentiate area
As it is given that
The radius of circular wave is 8 cm. Therefore,
Thus, the area is increasing at rate a of
