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

Given the statement: 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.

Since, aquarium is in the form of a rectangular solid.

Length of an aquarium(l) = 5 dm

Width of an aquarium(w)=
`(4)/(5)* 5 = 4 dm`

It is also given that when you put 40 liters of water into the aquarium, it was full to
`(2)/(3)` its volume.

Volume of Rectangular solid(V) is given by;

`V = l * b * h` where l is the length , w is the width and h is the height of the rectangle respectively.

Volume(V) of an aquarium =
`(3)/(2) * 40 = 60` liter.

Using volume formula to calculate the height(h);

`60 = 5 * 4 * h`

`60 = 20h`

Divide both sides by 20 we get;

h = 3 dm [ 1 liter = 1 cubic dm]

We have to find the what part of length makes up the height of the aquarium.

`h = (3)/(5) l` where l = 5 dm

therefore,
`(3)/(5)` part of the length makes up the height of the aquarium.