Question

let \\(a\\) be the area of a circle with radius \\(r\\). if \\(\frac{dr}{dt} = 2\\), find \\(\frac{da}{dt}\\) when \\(r = 3\\).

Explanation:

Relate area and radius of a circle

$$ A = \pi r^2 $$

Differentiate with respect to time

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

Substitute given values and solve

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Answer:

Let \(A\) be the area of a circle with radius \(r\). If \(\frac{dr}{dt} = 2\), find \(\frac{dA}{dt}\) when \(r = 3\).

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