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**Section 1.4 Metric Volume and Density**

Units of Measure Section 1.4 Metric Volume and Density

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**Pre-View 1.4 Volume – the amount of space an object occupies**

Cubic meter – the amount of volume in a box that is one meter long, one meter wide, and one meter high Liter – common metric unit used to measure liquid or gas volume Milliliter – the volume equal to one cubic centimeter (cm3)

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Pre-View 1.4 Water displacement – a method used to find the volume of an irregularly shaped object. Graduated cylinder – piece of equipment that can be used to find the volume of an irregularly shaped object. Density – the measure of mass per unit of volume; calculated by dividing mass by volume.

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Measuring Volume Volume is a measurement of three dimensions and is calculated by multiplying length, width, and height. For example, the volume of one cubic meter (m3) can be represented by a box that is one meter long, one meter wide, and one meter high.

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Measuring Volume Instead of using cubic units like m3 or cm3, volume can also be expressed in liters (L). One cubic centimeter is equal to one milliliter (mL). Solid volume is usually given in cubic meters or cubic centimeters, but gas and liquid volumes are commonly given in liters or milliliters.

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**Measuring Volume – Regularly Shaped Objects**

Regularly shaped objects are objects that are square, rectangular, cylindrical, cone-shaped, or spherical. By using a ruler to determine one or more of their dimensions, you can then use a formula to determine volume Example – to determine the volume of a rectangular object, measure each dimension. Then multiply the three dimensions together.

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**Measuring Volume – Regularly Shaped Objects**

For Example: Using a ruler, John determines his biology textbook is 25 centimeters wide, 30 centimeters long, and 3 centimeters thick. What is the volume of the textbook: 25 cm x 30 cm x 3 cm = 2250 cm3 The textbook’s volume is 2,250 cm3

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**Measuring Volume – Irregularly Shaped Objects**

Many objects are not perfectly rectangular. Water displacement can be used to obtain the volume of an irregularly shaped object. First, a known volume of water is recorded. Then the object is submerged in the water, and a water plus object volume is determined. The difference in the first volume and the second volume is the volume of the object.

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**Measuring Volume – Irregularly Shaped Objects**

Example Dr. Watts, a paleontologist, wants to know the volume of a fossilized bone. She measures exactly 10 mL of water in a graduated cylinder. She then drops the bone into the graduated cylinder. The volume of the water and the bone measures 12.5 mL. What is the volume of the bone?

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**Measuring Volume – Irregularly Shaped Objects**

Example (continued) 12.5 mL – 10 mL = 2.5 mL The bone has a volume of 2.5 mL, which is the same as 2.5 cm3.

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**SI unit of Volume: cubic meter (m3)**

When to use it… Use cubic meters for large volumes. Example: The water volume in an Olympic swimming pool is about 2500 m3

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**SI unit of Volume: liter (l)**

When to use it… Use instead of quarts or gallons. Example: A common size for a large soft drink container is 2 liters

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**SI unit of Volume: cubic centimeter (cm3) or milliliter (ml)**

When to use it… Use cubic centimeters or milliliters for small solid or liquid volumes. Example: A small cellular phone is about 90 cm3 A 20 ounce soft drink bottle holds about 590 ml

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Measuring Density Density is mass per unit of volume and is a common value measure in science. To get an idea of what density is, think about a marble and a small styrofoam ball that are the same size and have the same volume. The marble will sink in water, but the styrofoam ball will float.

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Measuring Density If they are the same volume, why does one sink and the other float? The answer is density. The marble is dense and has more mass in the same amount of volume than the styrofoam. In general, an object that has a density greater than the density of water will sink in water.

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Measuring Density An object having a density less than the density of water will float. Water has a density of one gram per milliliter (1 g/mL) To determine density of an object, you divide the mass of the object by the volume of the object. The resulting units are commonly g/cm3, kg/m3, g/mLor kg/L

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**Measuring Density Example**

In the previous example, Dr. Watts found the volume of a fossilized bone to be 2.5 mL. She determined that the mass of the bone is 9 grams. What is the density? Will it float or sink in water?

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