Question

A rectangular tank 60 cm long and 50 cm wide is /5 full of water. When 24 liters of water are added, the water level rises to the brim of the tank. Find the height of the tank. (1 liter is 1000cm3 )

Answer 1

The tank is 10cm high

Explanation:

Given

`L=60cm` -- length

`W=60cm` -- width

`x = (1)/(5)` --- water lever

`Addition = 24L`

Required

The height of the tank

Let y represents the remaining fraction before water is added.

So:

`y + x = 1`

Make y the subject

`y = 1 - x`

`y = 1 - (1)/(5)`

Solve

`y = (5 - 1)/(5)`

`y = (4)/(5)`

Represent the volume of the tank with v

So:

`y * v = 24L`

Make v the subject

`v = (24L)/(y)`

Substitute:
`y = (4)/(5)`

`v = (24L)/(4/5)`

`v = 30L`

Represent the height of the tank with h;

So, the volume of the tank is:

`v = lwh`

Make h the subject

`h = (v)/(lw)`

Substitute values for v, l and w

`h = (30L)/(60cm * 50cm)`

Convert 30L to cm^3

`h = (30*1000cm^3)/(60cm * 50cm)`

`h = (30000cm^3)/(3000cm^2)`

`h = 10cm`