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Question
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is ______.
Options
10π
12π
8π
11π
Solution
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is 12π.
Explanation:
If A is the area of the circle cooresponding to radius r, then
A = πr2
Differentiating with respect to r, `(dA)/(dr) = 2pi r`
Putting r = 6,
`(dA)/(dr) 2pi xx 6`
= 12 π cm2/sec
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