The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

Solution:

In maths, derivatives have wide usage.

They are used in many situations like finding maxima or minima of a function, finding the slope of the curve, and even inflection point

We know that

C = 2π r

Now,

dC/dt = d/dt (2π r)

= d/dr (2π r) dr/dt

On differentiating wrt t, we get

= 2π dr/dt

We have,

dr/dt = 0.7π cm/s [ given ]

Hence,

dC/dt

= 2π (0.7)

= 1.4π cm/s

Therefore, the rate of increase of its circumference is 1.4π cm/s

---

NCERT Solutions Class 11 Maths - Chapter 6 Exercise 6.1 Question 6

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

Summary:

Given that the radius of a circle is increasing at the rate of 0.7 cm/s. The rate of increase of its circumference is 1.4π cm/s