a.maths --hkcee 1992 (i need the full solution from hkeaa)

2007-09-24 4:39 am




There is a vessel in the shape of a right circular cone with semi-vertical angle 30°. Water is flowing out of the cone through its apex at a constant rate of π cm^3s^-1
a) Let Vcm^3 be the volume of water in the vessel when the depth of water is h cm. Express V in terms of h.
b) How fast is the water level falling when the depth of water is 4 cm?



回答 (1)

2007-09-24 10:19 am
✔ 最佳答案
There is a vessel in the shape of a right circular cone with semi-vertical angle 30°. Water is flowing out of the cone through its apex at a constant rate of π cm^3s^-1
a) Let Vcm^3 be the volume of water in the vessel when the depth of water is h cm. Express V in terms of h.
V = (1/3)[π (h tan30)^2] h = π h^3/9
b) How fast is the water level falling when the depth of water is 4 cm?
dV/dt = (π h^2/3) dh/dt
π = (π 4^2/3) dh/dt
dh/dt = 3/8 cm/s


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