CUET · MATHS · PYQ PAPER 2025
The rate of change of area of a circle with respect to its circumference when radius is 6 cm, is
- A \(2 \mathrm{~cm}^2 / \mathrm{cm}\)
- B \(4 \mathrm{~cm}^2 / \mathrm{cm}\)
- C \(6 \mathrm{~cm}^2 / \mathrm{cm}\)
- D \(12 \mathrm{~cm}^2 / \mathrm{cm}\)
Answer & Solution
Correct Answer
(C) \(6 \mathrm{~cm}^2 / \mathrm{cm}\)
Step-by-step Solution
Detailed explanation
\(A = \pi r^2\) \(C = 2\pi r\) \(\frac{dA}{dr} = 2\pi r\) \(\frac{dC}{dr} = 2\pi\) \(\frac{dA}{dC} = \frac{dA/dr}{dC/dr} = \frac{2\pi r}{2\pi} = r\) \(\frac{dA}{dC} = 6 \mathrm{~cm}^2 / \mathrm{cm}\)
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