The rate of change of area of a circle with respect to its circumference when radius is 4 cm, is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 cm2/cm
Let r be the radius. The area and the circumference are
\(A = \pi r^2,\quad C = 2\pi r\)
\(\displaystyle \frac{dA}{dr} = 2\pi r,\quad \frac{dC}{dr} = 2\pi\)
By the chain rule:
\(\displaystyle \frac{dA}{dC} = \frac{dA/dr}{dC/dr} = \frac{2\pi r}{2\pi} = r\)
At r = 4 cm:
\(\displaystyle \frac{dA}{dC} = 4 \text{ cm}^2/\text{cm}\)