# Distinguishing Between Surface Area and Volume

Warmup

Activity #1

`Compare and Contrast Surface Area and Volume of a 3-Dimensional Figure.`

The volume of a 3D shape is the space inside it, while the surface area of a 3D shape is the total area of all its faces. Surface area, or simple Area, covers the outer space and Volume covers the inner capacity. The Area is measured in square units and Volume is measured in cubic units. In the next activities, you will be interacting with applets to better understand the difference.

• With the sliders in the applet below, create a rectangular prism using the information below and record how many cubes it contains.
• Answer the questions that follow.

(1.) a = 1, b = 2, c = 3

(2.) a = 6, b = 5, c = 3

Activity #2

`Build Up Shapes Using Cubes.`

You are going to use the applet below to visually explore surface area and volume of a 3D rectangular prism.

• Adjust the sliders for “Length”, “Width” and “Height” to adjust the edge lengths of the rectangular prism.
• Use the “Create Net” slider to open up the prism and see the “net” which relates to the surface area.
• Use the “Options” slider to clearly see the parallel faces.

Activity #3

`Sketch a Prism and Find its Surface Area and Volume.`

In the following applets, you may want to draw the described prisms in order to calculate their surface area and volume. To draw a prism, follow the instructions below.

• Right click on the applet and choose . You now have a grid in the background.
• Feel free to rotate the plane to have a clearer view of the grid.
• Now, select the Polygon tool to draw the base of the prism with dimensions of your choice.
• Make sure you follow the grid lines to draw a base with accurate dimensions..
• Click on the Prism tool and select .
• Click on the base of the just created base. A click elsewhere won’t produce any results.
• Enter a height of your choice in the altitude box. (Enter only the number with no units.)
• Click Ok.
• Click to deselect. You now have a rectangular prism with the given dimensions.
• Now, click and click on each face of the prism to find its area. Use these values to find the surface area.
• Also click and click on the prism to find the volume.

(1.) A rectangular prism has a height of 1 cm and a base that is 3 cm by 5 cm.

(c.) Analyze the volumes and surface areas of the prisms. What do you notice? Write 1 or 2 observations about them.

(d.) Can you find more examples of prisms that have the same surface areas but different volumes? How many can you find?

(2.) A rectangular prism has a height of 1 cm and a base that is 1 cm by 11 cm.

(3.) A rectangular prisms has a height of 1 cm and a base that is 2 cm by 7 cm.

Quiz Time

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