Question

If A is the area of a circle with radiusr and the circle expands as time passes, find dA/dt in terms of dr/dt.

Answer 1

Answer:

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

Step-by-step explanation:

Your solution is correct (See explanation):

Area (A) of a circle is

$A = \pi r^2$

Where

$r = radius$

Differentiate both sides with respect to t

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

This is so because, we have to differentiate A on the left hand side and r on the right hand side because $2\pi$ is a constant

Hence, your solution is correct and and

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