Question

A rectangular tank 50 centimetres by 30 centimetres by 25 centimetres is 40 percent full of water. How many litres of water are needed to fill the tank completely?Volume of water needed = Volume of empty spaceHeight of empty space = ________ cm x 0.6 = ________ cmVolume of water needed= ________ cm x ________ cm x ____________ cm= ________ cm^3 = _______ mL = ____________ L_________ litres of water are needed to fill the tank completely.

Answer 1

22.5 liters

Step-by-step explanation

We know that the tank is 40% full of water. This means that 60% of the tank is empty, so the height of the empty space of the rectangular tank is,

`h_(empty)=h_(tank)\cdot(60)/(100)=h_(tank)\cdot0.6cm`

The volume of the empty space, since the tank is a rectangular prism, is the product of the empty space dimensions,

`V_(empty)=h_(empty)\cdot l_(empty)\cdot w_(empty)=0.6h_(tank)\cdot l_(tank)\cdot w_(tank)`

As we can see, the volume of the empty space is equal to 60% of the tank's volume,

`V_(empty)=0.6V_(tank)=0.6(50cm\cdot30cm\cdot25cm)=0.6\cdot37,500cm^3=22,500cm^3`

1 cubic centimeter is equivalent to 1 milliliter,

`V_(empty)=22,500cm^2=22,500mL`

Now, to transform from milliliters to liters, we have to divide this volume by 1000 or, in other words, move the decimal point 3 units to the left,

`V_(empty)=22,500mL=22.5L`

Hence, 22.5 liters of water are needed to fill the tank completely.