Let's start with the derived formula and the reworded problem:

dA dt = 2r

dr dt

Find the rate of change of radius given that the rate of change of area is 12 cm²/sec, at the instant when the radius is 10 cm. In Symbols, this is

Find dr dt given that

dA dt = 12 at the instant when r = 10.

Substituting these values in the formula gives

12 = 20

dr dt .

Solving for dr/dt gives the result,

dr dt = 12 20

=

3 5

cm/sec.

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