Question

a fish tank in the form of a rectangular solid is to accommodate 13 fish. if each fish needs 1512 cubic inches to live and the dimensions of the base of the tank are 39 inches by 12 inches what is the minimum height of the tank.

Answer 1

Each fish needs 1512 cubic inches to live. Since there are 13 fish, to find the minimum volume of the tank, we multiply 1512 by 13:

`1512in^3*13=19,656in^3`

We need a rectangular solid with a volume of at least 19,656 cubic inches.

The information we have about the tank is that the length of the base is:

`\text{length}=39in`

The width of the base is:

`width=12\text{ in}`

A representation of the situation is shown in the following diagram:

We need to find the height h of the tank.

For that, we use the formula for the volume of a rectangular solid:

`\text{volume}=\text{length}* width* height`

In this case, the volume has to be at least 19,656 cubic inches, the length is 39 in, the width is 12in, and the height is h:

`19656=39*12* h`

We can solve the multiplication 39x12:

`19656=468* h`

And then divide both sides by 468 in order to solve for h:

`(19656)/(468)=h`

Solving the division:

`42=h`

The minimum height of the tank has to be 42 inches.

Answer: 42 inches