Name: Period: V = lwh

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1 Density Unit Packet Name: Period: To begin we are going to start with volume. Volume is the amount of space something takes up. It is measured in units like cubic centimeters or milliliters. Those units are written in a shortened way like this: cm 3 or ml. There are different formulas or equations in math that help us find the volume of certain easy to measure objects. The volume of a cube, or the amount of space that a cube takes up, has an equation that looks like this: Volume cube = length x width x height A shortened version of this looks like this: V = lwh The length, width and height are three different distances of edges on the cube. 1. On the cube above, write the words: length, width and height, each along a different side of the cube. A rectangular prism is a shape that is similar to a cube, but it does not have the same length on all of its sides. Examples of rectangular prisms are books, boxes, houses and those sort of things. To solve for the volume of a rectangular prism, we use the exact same formula for the volume of a cube.

2 2. What is the formula for the volume of a rectangular prism or cube? 3. Write two units that we use for volume: Units for volume are for a three dimensional space. If it is hard to remember what they are on a specific problem you need to use one easy trick. When you write down a multiplication problem you write it by multiplying all of the numbers together. To remember the right units you can multiply them as well. For example: 2 x 2 x 2 = 8... but 2 cm x 2 cm x 2 cm = 8 cm 3 Notice the number three written small and higher next to the centimeter? 4. Circle the three that is next to the centimeter now. This three is there because the centimeter has been multiplied three times. This is called cubing or raising something to the third power. Milliliters is different though. We don't typically times or multiply a ml unit by another milliliter unit to get a volume of something because it is the entire volume of something already. One ml is equal to a cubic centimeter. We use milliliters to measure volumes of liquids. Take one of the measuring cups at your table or if you are at home grab one from the cupboard and examine the measurement on the cup. These cups have both English units (cups) as well as metric units (milliliters) cup is close to the same amount as how many milliliters?

3 6. What is the definition of volume? Solve the following problems for volume. Remember to include the correct units and you must show your work. Don't forget to use the trick of writing the units in your work! Each problem is worth 3 points. 7. Find the volume of the following rubik's cube. Show your work and include the correct units. 8. Find the volume of the Home Depot shipping crate. Show your work and include the correct units. 9. Find the volume of the UPS Express shipping box below. Show your work and include the correct units. 10. Find the volume of rectangular dog house below. Show your work and include the correct units. (Notice this box is not measured in cm! Pay attention and get the correct units!)

4 Now lets talk about mass. Mass is slightly tricky. It is defined by the amount of matter in something. So mass is the measure of the amount of matter in an object. For example, all of the matter that makes up a baseball would be considered the mass of a baseball. We use weight to describe the mass. Weight is extremely close to the same thing as mass. In fact, we use it interchangeably or in the place of mass all of the time. And since the weight of mass stays relatively stable anywhere on our planet we can get away with it. Ha, ha, ha, ha!... BUT, weight and mass are technically different. The weight of an object is the measurement of the mass under the force of gravity. So, for example, if you were to instantly transport yourself to the moon, your mass would stay the same. But, since the gravity on the moon is less, there is less of an effect of gravity on your mass and you would weight less. So, mass is the measure of matter in you; weight is the measure of mass under the force of gravity. Slight difference, but there is one all the same. 11. What is the definition of mass? 12. What is the definition of weight?

5 We determine an object's mass or weight on Earth by using a scale. In science we measure that mass or weight in metric units like grams or kilograms. This is just like weighing yourself on the bathroom scale in pounds, but instead of using the English unit pounds, we use the metric unit grams or kilograms. For example, you might weight about 100 pounds in English units, but in metric units you weigh 45.4 kilograms. You still weigh the same amount. Your weight or mass did not change, just the scale on which we weighed you changed. For our class, we will not be using pounds, but instead we will use grams or kilograms. 13. Go to the front of the room where the scale is. On this scale it will show your pounds in English units as well as kilograms in metric units. Record your weight in both pounds and kilograms below. (If you are doing this packet at home, use your bathroom scale and switch it to kilograms or metric. If you scale doesn't have this option, go to google and type in the search bar: your weight in pounds or 103 pounds =? kg. Google will automatically calculate your weight for you.) Your weight: pounds kilograms Now we are going to venture into density. Density is complicated for a few people. But, it is a simple concept. Density is how compact something is. An object with a higher density has it's matter closely packed together. It is NOT the weight of an object. But objects that have a high density are

6 heavy. Objects with a low density are light. The density of air is very small. Its atoms and molecules are spaced far apart from one another. Air is not very compact. The density of a rock is high because the atoms and molecules or matter are closely pack together. 14. Which is more dense or more compact, the air or a rock? even though it is smaller than the cotton candy, it weighs much more. We use density to compare objects with each other in order to see which is more compact. If objects are of different sizes we can't just weigh them to discover which is more dense. Think about a boulder chasing after Indiana Jones. That boulder is probably pretty heavy and would squash anyone in its path. But we can't compare its density to a small pebble by weighing them. The boulder will weigh much more than the small pebble even if the boulder is pumice and the pebble is solid metal. We don't know if the pebble is more compact than the large boulder unless we can compare their densities. We find the density of an object by using another mathematical formula or equation. The formula for density is: mass density = volume Remember that mass will be interchangeable with weight for our problems here

7 and will be measured in grams for our class. Volume is the amount of space something takes up. So if we take the weight of an object and compare it with the space the object takes up we can determine how compact an object is or the object's density! 15. What is the definition of density? 16. What is the equation to solve for density? 17. In our class, what will be the units we will use for mass? 18. What two things do you need to be able to solve for density? Density will be calculated using mass divided by volume. Units are a hard thing for people to remember, but if you use our simple trick from earlier and write the units in your work as you solve the problem it becomes much easier. For example: density = mass volume So... if my mass of a ball is 150 grams and the volume of that ball is 100 cm 3 then I can start to solve my equation by listing the known variables or pieces of the equation that I have. mass = 150 g volume = 100 cm 3 if in my problem mass divided by volume is equal to density, then I can do a simple division problem by substituting my known variables in the right locations. 150 g Density = 100 cm 3 By putting my units in my problem I can see the units of density in the equation! Grams divided by cubic centimeters or grams per cubic centimeters. We write them like this: g/cm 3. Density = 1.5 g/cm 3 To solve the equation we simply need to divide the numbers and write the correct units in our answer. The complete answer is 1.5 g/cm 3.

8 We can also use the units for liquid volume. If you remember from earlier, liquid volumes can be represented in ml. One milliliter is equal to a cubic centimeter. Sometimes objects are weirdly shaped and we can't take easy measurements of them. A rock is a good example of an oddly shaped object that we can't really measure with a ruler. To do this we use water displacement. Water displacement is a technique to measure the amount of water that gets pushed out of the way when we drop an object into water. Think about when you take a bath and your tub is full of water. When you get up out of the tub, the water level goes down. When you get back in, the water level goes up. This is because you have volume to. You also take up space. When you enter the tub the water is displaced or moved out of the way for your body, or your volume. When you do this the water rises. It rises the exact amount or volume that your body is. We can measure this displacement of the water by using a graduated cylinder. First we fill it with water to a measurement. Next we drop the odd object into the water. Then we see just how much water moved out of the way for the odd object and we write down that measurement in milliliter or ml. This is the full volume measurement of the odd object with no mathematical calculations needed! YAY! So density can be expressed in two ways, either in units of g/cm 3 or g/ml. 19. What are two units of density? 20. What are two units of volume that are equal to each other? Now its time to calculate some density problems. Solve the problems below for density. Watch for tricky questions that may need you to solve to volume first and then density second. Stay sharp, show your work, and don't forget the proper units. Each

9 problem is worth 3 points. 21. The volume of the Home Depot crate below is 1,000,000 cm 3. Its mass is 1,000,000 grams. What is the box's density? Start by writing the equation for density: then write your variables: mass = volume = Now substitute the variables into the equation and solve for density. 22. The volume of a metallic cube is 1,000 cm 3. Its mass is 2,500 grams. What is the density of the cube? (use the same steps as above to help you and don't forget your units!) 23. A cube has a width of 2 cm. Its mass is 64 grams. What is the density of the cube? (be careful and pay attention to the cube's size)

10 24. What is the density of the liquid below? 25. Use the following information to find the density of the rock. 26. Use the following information to find the density of the rock. 27. What is Density? (Describe in words, not how to calculated it) If you have answered each and every question in this packet and obtained a 90% or better on it, you are ready to move on. If, however, you have made a few mistakes, then you will need to go back and correct them until you have obtained the 90% score. Once you have done this, you are ready to take the density quiz! Good luck and may the force be with you!