Volume
Take a minute and consider the following:
 You have 2 empty containers.
One has a volume of 5 L and
the other has a volume of 3 L.
Neither has any markings.
 Your job is to find a way to fill
one container with exactly 4
L of water. You can fill a
container, empty a container and pour water from one to the
other without spilling over.
Write your thoughts in your notebook or discuss them with a neighbor.
What are our thoughts for this problem?
Definitions:
 Volume
o The amount of space a 3D object takes up
 Capacity
o The maximum amount a container can hold
Sometimes regular measurements like ft or cm are used to measure
volumes in units like ft3 or cm3. Other times there are specific units
used specifically for volume:
 Imperial
o Fluid Ounce = fl oz
o Pint = pt
o Quart = qt
o Gallon = gal
 SI
o Milliliter = mL
o Liter = L
Below are some common conversions you’ll need for these units:
US Imperial
1 fl oz
1 pt = 16 fl oz
1 qt = 2 pt
1 gal = 4 qt
1 gal
SI
29.6 mL
473.5 mL
947.2 mL
3788.8 mL
3.79 L
1 L = 1000 mL
Notice that the chart says US Imperial. The reason for that is the US
imperial system isn’t exactly the same as the British imperial system.
 Ex. 1 US gal = 3.79 L, but 1 gal = 4.55 L
Naturally this changes many of the other conversions. For our course,
you only need to be aware there’s a difference, but our calculations will
focus on SI and US Imperial measurements.
When cooking, there are a few other units you need to be aware of as
well:
US Imperial
1 tsp
1 tbsp = 3 tsp
1 cup
SI
4.9 mL
14.7 mL
236.6 mL
Examples:
 Nigel has a car with a 22 gal gas tank. How many liters is this?
How much would it cost to fill if gas were $1.20/L?
o All we need to do is convert gallons to liters and then
multiply that by the price per liter.
? 𝐿𝑖𝑡𝑒𝑟𝑠
22
=
3.79 𝐿
1 𝑔𝑎𝑙
? 𝐿𝑖𝑡𝑒𝑟𝑠 = 22 × 3.79 ÷ 1 = 83.38 𝐿
Cost to fill = 83.88 L x $1.20/L = $100.06
So the car has a tank that will hold roughly 83.4 L and it
would cost $100.06 to fill.
1
 Rita built a wood planter that is 4 ft long, 2 ft deep and 1 ft wide.
2
She needs to buy dirt to fill it and the store she checks sells it for
$21.50/m3. How much would the dirt cost her?
o First I need to know the capacity of the planter so I know
how much dirt she needs.
1
4 x 2 x 1 = 12 ft3
2
o Since the price is in m3 I will convert the capacity into that
unit. To do this I need to know how many ft are in a m and
then calculate how many ft3 are in a m3.
1 ft = 30.48 cm and 100 cm = 1 m
100 ÷ 30.48 = 3.28  so there should be 3.28 ft in 1 m
1 m3 = 1 m x 1 m x 1 m = 3.28 ft x 3.28 ft x 3.28 ft = 35.3 ft3
o Now to convert ft3 into m3
? 𝑚3
12𝑓𝑡 3
3
=
1 𝑚3
35.3 𝑓𝑡 3
? 𝑚 = 12 × 1 ÷ 35.3 = 0.34 𝑚3
o Now that I know how many m3 of dirt she needs, I’ll multiply
that by how much it costs.
0.34 m3 x $21.50 per m3 = $7.31
So the dirt will cost Rita $7.31.
Let’s try a few together:
 Convert 3 US gal to liters. (11.37 L)
 Convert 500 mL to tablespoons. (34 tbsp)
 Convert 1.3 m3 to yd3 (1.7 yd3)
Practice
Complete questions 1-5 on P.132 of the textbook.