1. Displacement and Density Section 10.5 April 12, 2005

2. Answers to Homework Page 543: 6. 3456  12. r = 9 in. 16. The golf ball is 10.6  ; the volume left in the cylinder is 16  ; so the water will not overflow. Page 547 5. V = 256/3   85.3  6. S.A. = 144 .

3. Displacement What happens when I add ice cubes to a glass of soda? What happens when you put a scoop of ice cream in some root beer? What happens if you put your dog in the tub full of water for a bath?

4. All of these are examples of DISPLACEMENT, which means that the water is displaced by an object when it is placed in water.

5. Displacement You can use displacement to find the volume of any object, especially objects of irregular size that we cannot measure with a formula. We just have to put them in an object filled with water in a container we can find the volume of!

6. DEMONSTRATION

7. Find the volume of the rock. Volume of water in square prism BEFORE inserting rock: –V = BH = (4 in)(4 in)(____) = Volume of water AFTER: –V = BH = (4 in)(4 in)(____) = What is the volume of the water DISPLACED? –V after – V before = _____ What is the volume of the rock? _____

8. Find the volume of the object. Volume of water in cylindrical container BEFORE inserting object: –V = BH =  r 2 H =  (2 in) 2 (____) = _______ Volume of water AFTER: –V =  r 2 H =  (2 in) 2 (____) = _______ = What is the volume of the water DISPLACED? – V after – V before = _____ What is the volume of the object? What is another way to find the displaced volume? What changes as you insert the object?

9. So to find the volume using displacement: V = BH where B is the area of the base of the container (prism or cylinder) and H is the change in the height of the water. Example: When you place a clump of metal into a container of water, it raises that water level by 5 cm. If the container is a rectangular prism whose base measures 15 cm by 15 cm, what is the volume of the metal?

10. Archimedes, Again! A king once gave him a difficult task. The king had a crown. He had paid for pure gold. He was afraid that the crown-maker had mixed silver with the gold. He wanted Archimedes to figure out whether or not the crown was pure gold or mixed with silver. Now, you know that all he had to do was to figure out the density of the metal. Silver's specific gravity is 10.5 and the specific gravity of gold is 19.3. It should be easy to detect the difference. The problem was to determine the volume of the crown. The kind did not want Archimedes to harm the crown in any way. How do you calculate the volume of a crown?

11. Finding Density Density is the mass of matter in a given volume. Density is the ratio of the mass of a substance to its volume, and it can be calculated by dividing the mass by the volume. Density is often expressed in units such as grams per cubic centimeter (g/cm 3 ) or pounds per cubic foot (lb/ft 3 ). Density = Mass / Volume

12. Density Table MetalDensityMetalDensity Aluminum2.81 g/cm 3 Nickel8.89 g/cm 3 Copper8.97 g/cm 3 Platinum21.40 g/cm 3 Gold19.30 g/cm 3 Potassium0.86 g/cm 3 Lead11.30 g/cm 3 Silver10.50 g/cm 3 Lithium0.54 g/cm 3 Sodium0.97 g/cm 3

13. Calculating Density Archimedes places the crown in a cylindrical container full of water of radius 6 cm, and notices that the water level rises 1.1 cm. He weighs the crown and notices that it weighs 2401.05 grams. Is the crown made of gold? –Mass = 2401.05 g –Volume = V =  r 2 H =  (6 cm) 2 (1.1 cm) = _______ –Density = Mass / Volume = __________

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