Question

Hank has just purchased a small rectangular fish tank that holds 950.4 milliliters of water. The tank has a width of 8.8 cm and a height of 9 cm. what is the length of the fish tank?

Answer 1

We will investigate how to determine one of the indicator dimensions of a regular figure.

We have a rectangular fish tank which can be modeled as a cuboid. The indicator lengths of a cuboid or a rectangular fish tank are as such:

`\begin{gathered} \text{Length ( L ) } \\ \text{Width ( w ) = 8.8 cm} \\ \text{Height ( h ) = 9 cm} \end{gathered}`

One of the indicator lengths of the rectangular fish tank Length ( L ) is unknown. Howver, we are given the total amount of water that the fish tank can withold as follows:

`\text{Water in fish tank = 950.4 mL}`

We will use the conversion factor between milliLiters and centimeter cube as follows:

`1\text{ mL }\to1cm^3`

Therefore,

`950.4\text{ mL }\to950.4cm^3`

The amount of water a fish tank can hold is equivalent to the volume of the fish tank. We have modeled our rectangular fish tank as a cuboid. The volume ( V ) of a cuboid can be expressed in terms of its indicator dimensions as follows:

`V\text{ = L}\cdot w\cdot h`

We can use the above volume expression to determine one off our missing indicator dimension of length ( L ). We plug in the respective quantities and evaluate:

`\begin{gathered} 950.4\text{ = L}\cdot(8.8\text{ ) }\cdot\text{ ( 9 )} \\ \\ L\text{ = }(950.4)/(8.8\cdot9)\text{ = }(950.4)/(79.2) \\ \\ L\text{ = 12 cm} \end{gathered}`

Therefore, the length ( L ) of the fish tank must be:

`12\text{ cm }\ldots\text{ Answer}`