Question

If by dropping a stone in a quiet lake, a wave moves in circle at a speed of $3.5cm/sec$, then the rate of increase of the enclosed circular region when the radius of the circular wave is $10cm$.
($\pi =\frac{22}{7}$)

• A. $220{cm}^2/sec$
• B. $110{cm}^2/sec$
• C. $35{cm}^2/sec$
• D. $350{cm}^2/sec$

Answer 1

The correct option is A $220{cm}^2/sec$

$A=\pi r^2$

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

$=2\times \frac{22}{7}\times \frac{35}{10}\times 10$

$220c{m}^2/s$