The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
(A) 10π   (B) 12π   (C) 8π   (D) 11π

Solution:

Derivatives are used to find the rate of changes of a quantity with respect to the other quantity. By using the application of derivatives we can find the approximate change in one quantity with respect to the change in the other quantity.

We know that Area of circle is given by  π r²

Therefore,

dA/dr = d/dr (π r²)

= 2πr

When r = 6 cm

Then,

dA/dr = 2π × 6

= 12π cm²/s

Thus, the rate of change of the area of the circle is 12π cm²/s.

Hence, the correct option is B

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.1 Question 17

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is (A) 10π (B) 12π (C) 8π (D) 11π

Summary:

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is 12π cm²/s. Hence, the correct option is B