The radius of a circle is increasing at the rate of 0.7 cm/sec. What is the rate of increase of its circumference?
Given: the radius of a circle is increasing at the rate of 0.7 cm/sec.
To find rate of increase of its circumference
Let the radius of the given circle be r cm at any instant time.
Then according to the given criteria,
Rate of radius of a circle is increasing is,
Then the circumference of the circle at any time t will be
C = 2r cm.
Applying derivative with respect to time on both sides we get,
[from equation(i)]
Hence the rate of increase of the circle’s circumference will be 1.4 cm/sec