## Unit Conversions Volume

Look at the table below and memorize the metric conversions of all units used to measure length.

k
 Common Volume Conversion Factors 1 cubic centimeter = 1000 cubic millimeter 1 cubic decimeter = 1000 cubic centimeter 1 cubic meter = 1000 cubic decimeter 1 liter / litre = .001 cubic meter 1 liter / litre = 10 deciliter 1 deciliter = 10 centiliter 1 centiliter = 10 milliliter 1 cubic foot = 1728 cubic inches 1 cubic yard = 27 cubic feet 1 fluid minims = 61.61152 cu mm 1 fluid drams = 60 minims 1 fluid ounces = 8 fluid drams 1 pint (pt) = 16 fluid ounces 1 gills (gi) = 0.25 pint 1 quart (qt) = 2 pint 1 gallon (gal) = 4 quart 1 oil barrel = 42 gallons

In order to convert metric units into English units and other units of measurements, we will use the
conversion factors stated above. Notice that we always use 1 unit of the length to be converted. Once this
is known, the conversion factor, we can then use this to multiply against a unit we wish to be converted.

REMEMBER

When going from a large unit to a small unit, you multiply.

When going from a small unit to a large unit, you divide.

There is another way of converting units. It is often called the long way because you need to arrange the values
to make a ratio and proportion equation. For example:

1. If 1 gallon = 4 quarts, how many gallons will there be in 20 quarts?

(1 gallon / 4 quarts) = (x gallons / 20 quarts)

1 gallon x 20 quarts = 4 quarts

X = 5 quarts

2. Today, the price is 3.4 AED/liter. If Jessie filled up her car with 40 deciliter quarts of gasoline,
(a) what is the volume she purchased in liters? (b) how much did she pay for this?

(a) Convert dL to L

(1 L / 10 dL) = (x / 40)

(40 / 10) = 4 L

b) (3.4 AED / L) = (x / 4)

3.4 x 4 = x

13.6 AED = x

3. A pint of beer costs \$8. Jack and his four friends bought 3 pints each.
(a) How many quarts of beer did they consume in total? (b) How much did they pay in total?

Total pint consumed = 12 pints

a) (1 pint / 2 quarts) = (12 / x)

x = 12 x 2

x = 24 quarts

b) 12 x 8 = \$96

#### Try these questions

1. A cough syrup has a dosage of 250 mg/5 mL of the prescribed antibacterial. The doctor calls for 750mg
to be taken twice daily. What is the total volume to be taken?

Explanation:

Use ratio and proportion first to find out the volume of one dose:

(250 mg/5 mL) = (750 mg / x mL)

x mL = 15 mL

Twice daily: 15 mL x 2 = 30 mL total volume to be taken

2. During renovation, the two painters used up 1/3 of the 10 pint red paint.
How many fluid ounces of red paint were used up?

Explanation:

1/3 x 10 pint = 3.33 pint

Convert pint to fluid ounce

(1 pint / 16 fluid ounces) = (3.33 pint / x)

X= 16 fluid ounces x 3.33 pint

X = 53.28 fluid ounce

3. The sum of the lengths of all sides of a cube is 8 cm. What is its volume? (Volume = l x w x h).

Explanation:

Since a cube has 12 sides, we get:

12e = 8

e = 8/12 or 2/3

Therefore, its volume is: e3

(2/3) x (2/3) x (2/3) =1.99 or 2 cm.

4. Jessie diluted 3L of mango puree with 4340 mL of distilled water. What is the resulting volume of the
mixture in mL?

Explanation:

Convert L to mL

(1 L / 1000 mL) = (3L / x mL)

X = 3000 mL