Question

The length of an aquarium, which has the form of a rectangular solid, is equal to 5 decimeters, and the width is 4/5 the length. When you put 40 liters of water into the aquarium, it was full to 2/3 its volume. What part of the length makes up the height of the aquarium? (1 liter is equal by volume to 1 decimeter3)

Answer 1

`(3)/(5)` of the height makes up the height.

Explanation:

The length of an aquarium, which has the form of a rectangular solid, is
`5\ dm`

The width is
`(4)/(5)` of the length, so teh width is,

`=5* (4)/(5)=4\ dm`

Let us assume the height is 'h' dm.

So the volume will be,

`=\text{Length }\cdot \text{ Width }\cdot\text{ Height}`

`=5* 4* h`

`=20h\ dm^3`

As 1 liter of water occupies volume of 1 dm³, so volume of 40 liters of water will be,

`=40* 1=40\ dm^3`

This
`40\ dm^3` is the
`(2)/(3)`th of total volume.

Hence total volume will be,

`=(40)/((2)/(3))=40* (3)/(2)=60\ dm^3`

Therefore,

`\Rightarrow 20h=60`

`\Rightarrow h=3\ dm`

So the part of length makes up to the height will be,

`=(3)/(5)`