Water flows in a tank 150 m x 100 m at the base through a pipe whose cross-section is 2 dm x 1.5 dm at the speed of 15 km/h. In what time, will the water be 3 m deep?

Concept Used:

The volume of cuboid = lbh

Where l = length of the cuboid, b = breadth of the cuboid, and h = height of the cuboid.

Given:

The speed at which water flows = 15 km/h

Length of the tank = 150m

The breadth of the tank = 100 m

The depth of the water = 3 m

Length of the pipe = 2 dm = 20 m

Breadth of the pipe = 1.5 dm = 15 m

(1 dm = 10 m)

Explanation:

The volume of the water = Volume of the tank when filled with water till 3 m

Volume of the water = (150 × 100 × 3) m³

The volume of the water through pipe = 20 × 15 × h

Where h = length of the pipe

The total volume of water remains the same.

Therefore, 150 × 100 × 3 = 20 × 15 × h

h

h = 150 m

Now,

Time = Speed × Distance

Time = 150 × 15 = 2250 hours.

Hence, the time taken to fill the tank is 2250 hours.