#@Application of Differentiation#(F.5)

Question

Red ink is poured onto a white shirt forming a circular stain on it .The area of the stain grows a steady rate of 1 cm^2 /s. Calculate , in terms of π,

a) the radius ,in cm , of the stain 4 seconds after the ink first touched the shirt,

b)the rate , in cm/s , of increase of the radius of the stain at this instant.

Answer 1

最愛解答

a)

After 4 seconds, the area of circle = 4*1 = 4 cm²

The radius = √(4/π) = 2/√π cm (or 1.13 cm in 3 sig. fig.)

b)

Let A be the area of the circle and r be its radius.

Then A = πr²

dA/dt = 2πr dr/dt

Since the area of the stain grows a steady rate of 1 cm² /s, dA/dt = 1

1 = 2πr dr/dt

dr/dt = 1/(2πr)

Since at that moment, r = 2/√π,

dr/dt = 1/[2π 2/√π] = 1/(4√π) cm/s (or 0.141 cm/s in 3 sig. fig.)

Hope it helps! ^^

資料來源： Myself