SOLUTION: Josephine fills up a swimming pool, measuring 30 m by 16 m, using a hose of radius 6 cm. If the pool is flat and the water flows at 18 km/h, what will be the depth of water (in cm)

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Josephine fills up a swimming pool, measuring 30 m by 16 m, using a hose of radius 6 cm. If the pool is flat and the water flows at 18 km/h, what will be the depth of water (in cm)      Log On


   

Question 825275: Josephine fills up a swimming pool, measuring 30 m by 16 m, using a hose of radius 6 cm. If the pool is flat and the water flows at 18 km/h, what will be the depth of water (in cm) in the pool after 2.5 hours? Round off your answer to 3 significant figures.
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Do everything in meters, and convert to centimeters for height at the end of the process.

Flow rate is in terms of length of water as if it were a tube. Cross section area is pi%2A0.06%5E2 m%5E2 and for 2.5 hours of flow time, this is a volume of
508.938%2Ameter%5E3

Now, what is the height in the tank in meters?
Let h = height in meters, to be later converted into centimeters;
30%2A16%2Ameter%2Ameter%2Ah%2Ameter=508.938%2Ameter%5E3
highlight%28h=508.938%2F%2830%2A16%29%2Ameter%29
h=1.06 meters, or 106 centimeters.