Question

The capacity of a cuboidal tank is 50000 liters of water. Find the breadth of the tank, if its length and depth are respectively 2.5m and 10m.

Answer 1

Hint: Volume of a cuboid with length, breadth and height as l, b, h can be given by relation \[l\times b\times h\]. And use the relation that \[1{{m}^{3}}\]= 1000 L to convert the volume into L or L to \[{{m}^{3}}\]whatever required.

Complete step-by-step answer:
We know the volume of a cuboid with length ‘a’, breadth ‘b’ and depth ‘h’ can be given by relation.
Volume of cuboid = \[l\times b\times h\]- (i)
Now, we know the volume of a solid represents its capacity, so the capacity of the cuboidal tank (50,000 litres) is representing its volume. Hence, we have
Volume of the given tank = 50,000L.
Now, we can change the volume in ‘L’ to ‘\[{{m}^{3}}\]’ by changing the units using relation.
\[1{{m}^{3}}=1000L\]
Hence, we can divide the above relation by 1000; so we get,
\[1L=\dfrac{1}{1000}{{m}^{3}}\].
So, we can convert the given volume in ‘L’ to \[{{m}^{3}}\]using the above relation.
Hence, 1L has \[\dfrac{1}{1000}{{m}^{3}}\]volume.
So, 50,000L volume will have \[=50,000\times \dfrac{1}{1000}{{m}^{3}}=50{{m}^{3}}\].
So, the volume of the tank in \[{{m}^{3}}\]is \[50{{m}^{3}}\].
Now, it is given that the length and depth of the cuboidal tank are 2.5m and 10m respectively. So, let breadth be ‘x’ m. Hence, we can get volume of the cuboidal tank using equation (i). Hence, we get
Volume of the tank \[=x\times 2.5\times 10=25x\].
As, we already have the volume of the tank as \[50{{m}^{3}}\]. Hence, we get
\[25x=50\]
\[x=\dfrac{50}{25}=2m\]
Hence, the breadth of the tank is 2m.
So, the answer is 2m.

Note: One may calculate the volume of the cuboidal tank is \[{{m}^{3}}\]and convert it to liters as well and hence equate it to given volume 5000L.
One may get confused with the term capacity and think it as a total surface area of the cuboid as well and may apply formula \[2\left( lb+bh+hl \right)\]which is wrong. So, be clear with the terminologies for solving these kinds of questions.