Question

If $A={\mathrm{\pi r}}^2$,and A and r are both functions of time t,find$\frac{dA}{dt}$

Short answer

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

Step-by-step solution

Step 1:Given information

The given expression is$A={\mathrm{\pi r}}^2$

Step 2:Simplification

$A={\mathrm{\pi r}}^2$

Step 2:Simplification

$A={\mathrm{\pi r}}^2$

Differentiating w.r.t t

width="160" height="41" role="math">dAdt=dAdr×drdt...(1)

width="140" height="41" role="math">⇒dAdr=2πr...(2)

Now,from equation $\left(1\right)$and$\left(2\right)$

width="126" height="41" role="math">⇒dAdt=2πrdrdt