Question

the radius r and area a of a circle are related by an equation a= pie r squared. write and euation the relates da/dt to dr/dt

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Answer 1

Step-by-step explanation:

dA / dt = 4πr [ dr / dt ]

Here is your Answer

Answer 2

Answer:

Recall that the area of a circle is:

$a = \pi {r}^{2}$

Therefore, we can write the area as:

$a(t) = \pi [{r} ({t})]^{2}$

Let us now take the derivative of both sides:

$\frac{da(t)}{dt} = \pi \times \frac{d}{dt} \pi [{r} ({t})]^{2}$

Here, the chain rule of differentiation takes effect. We take the derivative of the expression and then multiply the derivative of r with respect to t. We will get:

$\frac{da}{dt} 2\pi \: r \times \frac{dr}{dt}$