The rate of change of the area of a circle with respect to its radius \(r\), when \(r = 3\) cm, is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(6\pi\ \text{cm}^2/\text{cm}\)
The area of a circle is \(A = \pi r^2\), so its rate of change with respect to r is the derivative
\( \displaystyle \frac{dA}{dr} = 2\pi r \)
At \(r = 3\):
\( \displaystyle \frac{dA}{dr} = 2\pi \times 3 = 6\pi\ \text{cm}^2/\text{cm} \)
NCERT (2026-27 edition):
Rate of Change of Quantities
