# 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

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