The rate of change of area of a circle with respect to its circumference when radius is 6 cm, is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 cm2/cm
Let r be the radius. The area and the circumference are
\(A = \pi r^2,\quad C = 2\pi r\)
Both depend on r, so by the chain rule:
\(\displaystyle \frac{dA}{dC} = \frac{dA/dr}{dC/dr}\)
\(\displaystyle = \frac{2\pi r}{2\pi} = r\)
At r = 6 cm:
\(\displaystyle \frac{dA}{dC} = 6\) cm2/cm