A cuboidal tank has 25000 litres of water. If the depth of the cuboid is $\frac{1}{5}$ of its length and breadth is $\frac{1}{8}$ of its length, then the length of the tank is:

10 m

We know that,

Volume of a cuboid = lbh

We have,

Volume of tank = 25000 litres

Depth of cuboid = \(\frac{1}{5}\) of length

Breadth of cuboid = \(\frac{1}{8}\) of length

We also know, 1000 litres = 1 m³

25000 litres = 25 m³

Let the length of the tank = L

Depth of tank = L × \(\frac{1}{5}\) = \(\frac{L}{5}\)

Breadth of tank = L × \(\frac{1}{8}\) = \(\frac{L}{8}\)

Volume of a cuboid = L × \(\frac{L}{5}\) × \(\frac{L}{5}\) = 25

= L = 5 × 2 = 10 m