Question

Q1.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.

Answer 1

Step-by-step explanation:

Answer:

Area of circle = πr²

Using this relation, we are required to find the relation between (dA/dt) and (dr/dt).

Some formulae to be known while differentiating a variable w.r.t another variable:

$\boxed{\dfrac{d}{dx} (a) = a' \times \dfrac{da}{dx}} \:\: \implies \text{Chain Differentiation} </p><p>$

Differentiating the Area with respect to t, we get:

$\begin{gathered}\dfrac{d}{dt} (Area) = \dfrac{d}{dt} (\pi r^2)\\\\\\\implies \dfrac{dA}{dt} = \pi \times \dfrac{d (r^2) }{dt}\\\\\\\implies \dfrac{ dA}{dt} = \pi \times 2r \times \dfrac{dr}{dt}\\\\\\ \text{Applying the concept of Chain differentiation, we get:}\\\\\\ \boxed{ \bf{\dfrac{dA}{dt} = 2 \pi r \times \dfrac{dr}{dt}}}\end{gathered}$

Applying the concept of Chain differentiation, we get:

dA/dt=2πr×dr/dt

Hence this is the required relation.

Answer 2

Answer:

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