Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm   (b) r = 4 cm

Solution:

We know that the area of a circle, A = π r²

Therefore,

the rate of change of the area with respect to its radius is given by

dA/dr = d/dr (π r²)

= 2 π r

(a) When r = 3 cm

Then,

dA/dr = 2π (3)

= 6 π

Thus, the area is changing at the rate of 6π.

(b) When r = 4 cm

Then,

dA/dr = 2π (4)

= 8 π

Thus, the area is changing at the rate of 8π

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.1 Question 1

Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cm

Summary:

The rate of change of the area with respect to its radius when r = 3 is 6π and the rate of change of the area with respect to its radius when r = 4 is 8 π