Question

A fish tank of length, breadth and height 40cm, 60cm and 50cm respectively. It contains 50L of water. How much water is needed to fill the tank completely?
[a] 50L
[b] 60L
[c] 70L
[d] 120L

Answer 1

Hint: Use the fact that the volume of a cuboid of length l, breadth b and height h is given by V = lbh. Hence determine the volume of the fish tank. Use the fact that if ${{V}_{f}}$ is the volume of the fish tank in litres and ${{V}_{a}}$ is the volume of water added in litres, then ${{V}_{f}}={{V}_{a}}+50$. Hence determine the volume of the water to be added to fill the tank completely.

Complete step-by-step answer:

Let V be the volume(in litres to be added) to fill the tank completely.
Now, we have
The length of the tank (L) = 40 cm
Since 1m = 100cm.
Hence, we have
The length of the tank (L) $=\dfrac{40}{100}=$ 0.4m
Similarly, the breadth of the tank (B) = 0.6cm and the height of the tank (H) = 0.5m
We know that the volume of a cuboid of length L, breadth B and height H is given by V = LBH.
Hence the volume of the fish tank $=0.4\times 0.6\times 0.5=0.12{{m}^{3}}$
We know that 1 cubic metre = 1000 litres.
Hence, we have
The volume of the fish tank $=0.12\times 1000l=120l$
We know that if ${{V}_{f}}$ is the volume of the fish tank in litres and ${{V}_{a}}$ is the volume of water added in litres, then ${{V}_{f}}={{V}_{a}}+50$
Hence, we have
$120=V+50$
Subtracting 50 from both sides, we get
$V=120-50=70l$
Hence the volume of the water added to fill the tank completely is 70 litres.
Hence option [c] is correct.

Note: In the questions of mensuration, we need to take special care of units of the terms involved. If the units are not taken into consideration, we are likely to get incorrect results. In the above question, we needed to ensure that all the volumes were in litres to get the correct result. Many students forget that and end up with incorrect results.