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 decimeter^3)

Answer 1

Answer:

The height of aquarium is $\frac{3}{5}$ of its length

Step-by-step explanation:

It is given that the length of rectangular aquarium is 5 decimeter

width of aquarium = $\frac{4}{5}$ of length

                              = $\frac{4}{5} (5) = 4$ decimeter

so we have

width of aquarium = 4 decimeter

Let us assume the height of aquarium be x decimeter

so the volume of the aquarium = length × width × height

Volume of aquarium = 5(4)(x)= 20x decimeter³

it is given that 40 liters of water is $\frac{2}{3}$ of volume of aquarium

also

1 liter = 1 decimeter³

Therefore, 40 liters = 40 decimeter³

now we have

$\frac{2}{3}$ of volume of aquarium = 40

$\frac{2}{3}(20x)=40$

$\frac{40x}{3} =40$

multiply both side by 3

$40x= 3(40)$

$40x=120$

divide both side by 40

$x=\frac{120}{40}$

x = 3 decimeter

height of aquarium = 3 decimeter

comparing height and length

$\frac{height }{length} =\frac{3}{5}$

$height = \frac{3}{5} length$

hence the height of aquarium is $\frac{3}{5}$ of its length