Objectives: To investigate the volume of a prism, cylinder

Warm up Find the Base Area of: 1. a prism with length 5 in and width 6 in. 2. a cylinder with radius 4 in. 3. a rectangular pyramid with length 3 cm and width 6 cm. 4. a right cone with radius 2 cm.

Find the Volume of a Prism

Valentine’s Day is approaching. You have 48 chocolate cubes (1 in Valentine’s Day is approaching. You have 48 chocolate cubes (1 in. x 1 in. x 1 in.). How many ways are there to pack these 48 chocolates in the shape of a rectangular box? What are some possible sets of dimensions? I am trying to connect volume to something the students know. That’s why I choose chocolate cubes. To make it easier for the students I am using unit cubes so that the number of cubes equal the volume of the prism. The questions ask are essential questions to get the students to start thinking about dimensions and ways of getting the same volume with different dimensions. 4

How many cubes are in the prism? Make a one-layer rectangular prism that is 4 cubes long and 3 cubes wide. The prism will be 4 units by 3 units by 1 unit. How many cubes are in the prism? Click here to Check your answer It will be nice we can start off with 48 cubes to represent the chocolates cubes. If the students can play with them to arrange these cubes into rectangular prisms with different dimensions. As an example I am using a base of 3 x 4 cubes. 3 x 4 x 1 = 12 5

Add a second layer to your prism to make a prism 4 units by 3 units by 2 units. How many cubes are in the prism? Try again a. 36 cubes b. 12 cubes Try again c. 24 cubes Correct Interaction: Create a interaction where the second then 3rd and 4th level can be added when the students click on the interaction button. When the students click on a certain action buttons the cubes will fly in and form the 2nd, 3rd, and 4th layers. 6

Add a third and fourth layer to your prism to make a prism 4 units by 3 units by 3 units and 4 x 3 x 4. How many cubes are in the prism? Click here to Check your answer 3 layers: 3 x 4 x 3 = 36 4 layers: 3 x 4 x 4 = 48 Interaction: Create a interaction where the second then 3rd and 4th level can be added when the students click on the interaction button. 7

One way to pack the 48 chocolate cubes is 4 x 3 x 4. Is there another way to pack the 48 chocolate cubes? Students experiment with the 48 cubes to derive different dimension. Start off with 48 cubes, drag them to form a rectangular base of different dimensions until all the 48 cubes are done. Then write down the dimensions. 8

Notice that Base Area x Height is the Volume formula Notice that Base Area x Height is the Volume formula. Volume = Base Area x Height

How many cubes would be in the prism with base of 4 units by 3 units if there were 10 layers? The volume will be 4 x 3 x 10 = 120 cubes. The volume of a prism is equal to the length x width x height.

Now we learned that the volume of a rectangular prism is obtained by multiplying the Base Area with the Height. What happened if the prism change to a cylinder? How will you go about finding the volume of the cylinder?

What is the shape of the base? What is the area of a circular base? Examine the cylinder. What is the shape of the base? What is the area of a circular base? Then what will be the volume of a cylinder? Radius height I am trying to connect the volume of a prism to volume of a cylinder. The students always complain that there are too many formula to remember, now they need to remember only 1 formula i.e. volume = Area of the Base x height of the object. As long as the student is able to recognize the shape of the base and the corresponding area formula they can find the volume by multiplying the area with the height. 12

Then what will be the volume of a cylinder? Remember the volume of a prism is Area of the Base x height of the prism Now, consider the cylinder, the area of the cylinder base is r2, what is the volume of a cylinder?  r2 h 2 r 2 r h