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:

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)= $\frac{4}{5}\times 5 = 4 dm$

It is also given that when you put 40 liters of water into the aquarium, it was full to $\frac{2}{3}$ its volume.

Volume of Rectangular solid(V) is given by;

$V = l \times b \times h$ where l is the length , w is the width and h is the height of the rectangle respectively.

Volume(V) of an aquarium = $\frac{3}{2} \times 40 = 60$ liter.

Using volume formula to calculate the height(h);

$60 = 5 \times 4 \times h$

$60 = 20h$

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.

$h = \frac{3}{5} l$       where l = 5 dm

therefore, $\frac{3}{5}$ part of the length makes up the height of the aquarium.