# ####\$ Volume

## What is Volume?

Volume measures the three dimensional space inside of an object. While area measures how many flat squares can fit on a two dimensional surface, volume measures how many cubes can fit in a three dimensional space.

## Units of Volume

Volume is a measurement of three dimensional space and so the units of volume are also three dimensional. This means you will always label your answers with a cubed unit like $$mm^3$$, $$yd^3$$, or $$m^3$$.

If you were to find that a certain shape had a volume of $$9\, m^3$$, that means that there are nine cubes of space inside of the shape.

Volume is measured with cubes so the units of volume are three dimensional ($$in^3$$, $$cm^3$$, $$ft^3$$, etc).

Area is measured with squares so the units of area are two dimensional ($$in^2$$, $$cm^2$$, $$ft^2$$, etc).

Perimeter is measured with straight lines so the units of perimeter are one dimensional ($$in$$, $$cm$$, $$ft$$, etc).

## Real Life Examples

How much pasta is in the box?

What type of shape is the box?

The box is a rectangular prism.

What are the measurements of the box?

The measurements were not given to me, but I can make an approximation based on the size of the person’s hand.

So, I’ll say that the length of the box is $$\yellow 5\, in$$ and the width of the box is $$\yellow 4\, in$$ and the height is $$\yellow 3\, in$$.

$\yellow l=5$

$\yellow w=4$

$\yellow h=3$

How much pasta is in the box?

When I plug the length, width, and height of the box into the Volume of a Rectangular Prism Formula, I get…

$V=({\yellow 5})({\yellow 4})({\yellow 3})$

I can simplify the formula by multiplying $$\yellow 5$$, $$\yellow 4$$, and $$\yellow 3$$.

$V={\yellow 60}$

This means that there are $$\yellow 60 in^3$$ of pasta in the box.

I don’t really have a reference point for how much a cubic inch of pasta is. So, I could convert the cubic inches into cups or liters.

What type of shape is the box?

The box is a rectangular prism.

What are the measurements of the box?

The measurements were not given to me, but I can make an approximation based on the size of the person’s hand.

So, I’ll say that the length of the box is \(\green

How much water is in the glass?

What is…?