Find the amount of water

Cross section 3.6 m^2 flowing 10,000 m/hour. That's 36,000 cubic m of water in one hour. In half an hour, that will be 18,000. Divide by 0.08 meters to get 225000. It would have been nice to specify which unit to use, especially since they jump like 3 times but assume meters.

Actually this doesn't require use of calculus at all. It is an algebra question.

Solution

Velocity of water in the canal $= 10km/h = 100,000dm/h$

Hence, Volume of water pumped in half an hour $= \frac{30 * 12 * 100,000}{2} dm^3 = 18,000,000 dm^3$

Since height of the standing water is given as $8 cm$ or $0.8 dm$ and $Volume = area * height$ :

$Area = \frac{Volume}{height} = \frac{18,000,000 dm^3}{0.8 dm} = 22,500,000 dm^2 = \boxed{225,000 m^2}$

• 225000 squared metres.