A circular ink blot on a piece of paper increases its area at the rate (4mm^{2}/s). Find the rate of the radius of the blot when the radius is 8mm. ([pi = frac{22}{7}]).
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A.
0.20 mm/s -
B.
0.08 mm/s -
C.
0.25 mm/s -
D.
0.05 mm/s
Correct Answer: Option B
Explanation
Given: (frac{mathrm d A}{mathrm d t} = 4 mm^{2}/s)
(frac{mathrm d A}{mathrm d t} = (frac{mathrm d A}{mathrm d r})(frac{mathrm d r}{mathrm d t}))
(A = pi r^{2} implies frac{mathrm d A}{mathrm d r} = 2pi r)
(implies 4 = 2pi r times frac{mathrm d r}{mathrm d t})
(frac{mathrm d r}{mathrm d t} = frac{4}{2pi r} = frac{4 times 7}{2 times 22 times 8})
= (0.07954 mm/s approxeq 0.08 mm/s)