Question

An aquarium has a base in the shape of a trapezoid. The base is 80 cm long at the front, 50 cm long at the back, and 30 cm wide (from front to back). The height is 100 cm. What is the volume of the aquarium in litres?

Answer 1

The volume of the aquarium is 195 litres.

Explanation:

The volume (
`V`), measured in cubic centimetres, of the aquarium is equal to the area of the base multiplied by the height. That is:

`V = (1)/(2)\cdot (L+l)\cdot w\cdot h` (1)

Where:

`L` - Long leg length of the aquarium, measured in centimetres.

`l` - Short leg length of the aquarium, measured in centimetres.

`w` - Width of the aquarium, measured in centimetres.

`h` - Height of the aquarium, measured in centimetres.

If we know that
`L = 80\,cm`,
`l = 50\,cm`,
`w = 30\,cm` and
`h = 100\,cm`, then the volume of the aquarium is:

`V = (1)/(2)\cdot (80\,cm+50\,cm)\cdot (30\,cm)\cdot (100\,cm)`

`V = 195000\,cm^(3)`

If we know that a litre equals 195000 cubic centimetres, then the volume of the aquarium is:

`V = 195000\,cm^(3)* (1\,L)/(1000\,cm^(3))`

`V = 195\,L`

The volume of the aquarium is 195 litres.