A trough is 75cm long and its ends in the form of an isosceles triangle have an altitude of 20cm
and a base of 30cm. Water is flowing into the trough at the rate of 100cm3/sec. Find the rate at
which the water level is rising when the water is 10cm deep?
Let
- the current depth of the water layer.
The current volume of the water:
where is the base of the triangular cross-section of the water layer; this triangle is similar to the cross-section of the trough with similarity factor of , so .
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