Find the rate of change of the area of a circle with respect to its radius r when(a) `r = 3 c m` (b) `r = 4 c m`

Explanation

Let radius of circle be r and area be A.
Area A = `pi r^(2)`
`rArr (dA)/(dr) = pi (2r)`
(a) at r = 3 cm
` (dA)/(dr) = pi xx 2 xx 3 = 6 pi cm^(2)//sec`
(b) at r = 4 cm
` (dA)/(dr) = pi xx 2 xx 4 = 8 pi cm^(2) //sec`