The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
It is given that the radius of the circle is increasing at the rate of 3 cm/s uniformly.
Let the radius of circle be r cm .
The formula for the area of the circle is,
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 = 3 . Therefore,
d A d t = 2 π r ( 3 ) = 6 π r
Radius of circle is 10 cm. Therefore,
d A d t = 6 π ( 10 ) = 60 π cm 2 /s
Thus, the area of the circle is increasing at the rate of 60 π cm 2 / s .
It is given that the radius of the circle is increasing at the rate of
Let the radius of circle be
The formula for the area of the circle is,
Differentiate area
As it is given that
Radius of circle is 10 cm. Therefore,
Thus, the area of the circle is increasing at the rate of
