## 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?

Answer:

(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?

Answer:

(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?

Answer:

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?

Answer: 30 mL

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?

Answer: 53.28 fluid ounce

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).

Answer: 2 cm

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?

Answer: 7340 mL

Explanation:

Convert L to mL

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

X = 3000 mL

Add the two volumes:

3000 mL + 4340 mL = 7340 mL