Question

A rectangular water tank measures $15m\times 6m$ at top and is 10m deep. It is full of water initially. If water is drawn out, lowering the level by 1m, how much water has been drawn out?
[a] 90,000 litres
[b] 45,000 litres
[c] 4,500 litres
[d] 900 litres
[e] None of these

Answer 1

Hint: The amount of water drawn out = initial volume of the water inside the tank – the final volume of water inside the tank. Since water takes the shape of the container, it also will form a cuboidal block. Determine the dimensions of the cuboidal block of water initially and finally. Use volume of a cuboid of length l, breadth b and height h = lbh.

Complete step-by-step answer:
Since the water tank is initially full, the dimensions of the cuboidal block of water inside the tank initially are:
Length (l) = 15m, breadth (b) = 6m and height (h) = 10m.
Using the volume of cuboid = lbh, we get
The volume of water present inside the tank initially $=15\times 6\times 10=900$ cubic metres.
Now after drawing out of some water, the level of water lowers by 1m.
Hence, the new dimensions of the block of water are
Length (l) = 15m, breadth (b) = 6m and height (h) = 10-1 = 9m.
Hence, the volume of water inside the tank finally $=15\times 6\times 9=810$ cubic metres.
Hence the volume of water drawn out $=900-810=90$ cubic metres.
Now, we know that 1 cubic metre = 1000 litres.
Hence 90 cubic metres – 90,000 litres.
Hence the volume of water drawn out of the tank = 90,000 litres.
Hence option [a] is correct.
Note: Let H be the initial height and let d be the depth of lowering of water.
Hence final height = H-d. Let l and b be the length and bread of the tank.
The volume of water initially inside the tank = lbH.
The volume of water finally inside the tank = lb(H-d)
Hence volume of water drawn out of the tank = lbH-lb(H-d) = lbH-lbH+lbd = lbd.
This is equivalent to a cuboidal block of dimensions $l\times b\times d$ .
As can be observed the whole process is as if a cuboidal block of dimensions $l\times b\times d$ is removed from the original block. Hence the decrease in Volume = lbd.
Using d = 1m, l = 15m and b = 6m, we get
The volume of water drawn out of the tank $=15\times 6\times 1=90$ cubic metres, which is the same as obtained above.
It can be noted that the initial height of the water is not necessary to be provided to solve the question.