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 encoding area is increasing?

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 area of the circle is given by A = π r²

Now,

dA/dt = d/dt (πr²)

On differentiating wrt t, we get

= 2πr dr/dt

We have,

dr/dt = 5 cm/s

Hence,

dA/dt = 2πr (5)

= 10πr

So, when r = 8 cm

Then,

dA/dt = 10π (8)

= 80π cm²/s

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.1 Question 5

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 encoding area is increasing?

Summary:

Given that a stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s.The encoding area is increasing at 80π cm²/s