Class 12

Math

Calculus

Application of Derivatives

A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?

$r=10$cm

$A=πr_{2}$

$dtdA =dtdπr_{2} =πdtdr_{2} $

$=πdrdr_{2} dtdr $

$=π(2r)(4)$

$=2π10⋅4cm_{2}$/s

$=80πcm_{2}$/sec

answer