Question

If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dx/dt

Answer 1

The area of a circle in terms of the circle's radius
`r` is


`A=\pi r^2`

Differentiating both sides with respect to
`t`, you get


`(\mathrm dA)/(\mathrm dt)=2\pi r(\mathrm dr)/(\mathrm dt)`