A circle with radius 5cm has its radius increasing at the rate of 0.2m/s. What will be the corresponding increase in the area?
-
A.
2π -
B.
5π -
C.
π -
D.
4π
Correct Answer: Option A
Explanation
Area of the circle (A) = (pi r^{2})
(frac{mathrm d A}{mathrm d r} = 2pi r)
(r = 5cm); (frac{mathrm d r}{mathrm d t} = 0.2)
(frac{mathrm d A}{mathrm d t} = frac{mathrm d A}{mathrm d r} . frac{mathrm d r}{mathrm d t})
(frac{mathrm d A}{mathrm d t} = 2pi times 5 times 0.2 = 2pi)