Distinguishing Between Surface Area and Volume

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To Compare and contrast surface area and volume of a 3-dimensional figure.

With the sliders on the right, create a rectangular prism using the information below and record how many cubes it contains.

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

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

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To Build up Shapes using Cubes.

(A). This applet has 16 cubes in its hidden stack. Build two different shapes using 8 cubes for each.

(1). For each shape, give a name.

(2). For each shape, determine its volume.

(3). For each shape, determine its surface area.

(B). A rectangular prism has a height of 1 cm and a base that is 1 cm by 11 cm. Find the surface area and volume of the prism.

(C). The rectangular prisms has a height of 1 cm and a base that is 2 cm by 7 cm. Find the surface area and volume of the prism.

What is the surface area? What is the volume?

(D). 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:

  • MoSelect the Polygon tool to draw the base.
  • Then Select the Prism tool to create the rest of the prism.

The rectangular prisms has a height of 1 cm and a base that is 3 cm by 5 cm. Find the surface area and volume of the prism.

(1). What is the surface area? What is the volume?

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

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

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  • Use the WHITE VERTICES to alter the size of the composite solid shown below.​

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Lin said, “Two figures with the same volume also have the same surface area.”