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

Answer:

$\dfrac{3}{5}$ of the height makes up the height.

Step-by-step explanation:

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

The width is $\dfrac{4}{5}$ of the length, so teh width is,

$=5\times \dfrac{4}{5}=4\ dm$

Let us assume the height is 'h' dm.

So the volume will be,

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

$=5\times 4\times h$

$=20h\ dm^3$

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

$=40\times 1=40\ dm^3$

This $40\ dm^3$ is the $\dfrac{2}{3}$th of total volume.

Hence total volume will be,

$=\dfrac{40}{\frac{2}{3}}=40\times \dfrac{3}{2}=60\ dm^3$

Therefore,

$\Rightarrow 20h=60$

$\Rightarrow h=3\ dm$

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

$=\dfrac{3}{5}$