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

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 A = π r²

Now,

dA/dt = d/dr (π r²)

= 2πr dr/dt

We have,

dr/dt = 3 cm/s

Hence,

dA/dt = 2π r (3)

= 6π r

So, when r = 10 cm

Then,

dA/dt = 6π (10)

= 60 π cm²/s

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.1 Question 3

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

Summary:

Given that the radius of a circle is increasing uniformly at the rate of 3 cm/s. The rate at which the area of the circle is increasing when the radius is 10 cm is 60 π cm²/s