Question

The radius of a circular plate is increased at $0.01\text{cm/sec}.$ If the area is increased at the rate of $\frac{\pi }{10}$. Then its radius is

• A. $5$ cm
• B. $10$ cm
• C. $15$ cm
• D. $20$ cm

Answer 1

The correct option is A $5$ cm

Atp,

$\frac{dr}{dt}=+0.01$

$\frac{dA}{dt}=\frac{\pi }{10}$

$A=\Pi r^2$

$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$

$\frac{\pi }{10}=2\pi r\ast 0.01$

$r=\frac{1}{0.2}=5cm$