### Home > INT3 > Chapter 11 > Lesson 11.2.2 > Problem11-73

11-73.

Elliot has a modern fish tank that is in the shape of an oblique rectangular prism, shown at right.

1. Calculate the volume of water the tank can hold.

Use a special right triangle to find the height of the parallelogram.

Find the height of the parallelogram:

linear scale factor $= 6$

$h=6(1\sqrt{3})=6\sqrt{3}$

Find the volume:

$V = 7 \cdot 13 \cdot 6\sqrt{3} = 546\sqrt{3}$

$\approx 945.7\: \text{in.}^3$

2. If Elliot has $25$ fish, how crowded are the fish? That is, what is the density of fish measured in number of fish per cubic inch?

$\frac{\text{number of fish}}{\text{number of cubic inches}} =$

3. What is the density of fish in Elliot’s tank in fish per cubic foot?

Use dimensional analysis to convert

$\frac{\text{number of fish}}{\text{in}^3} \text{ into } \frac{\text{number of fish}}{\text{ft}^3}$