Lesson 16: Distinguishing Between Surface Area and Volume

Let’s contrast surface area and volume.

16.1: Attributes and Their Measures

For each quantity, choose one or more appropriate units of measurement.

For the last two rows, think of a quantity that could be appropriately measured with the given units.

Quantities

  1. Perimeter of a parking lot: 
  2. Volume of a semi truck:
  3. Surface area of a refrigerator:
  4. Length of an eyelash:
  5. Area of a state:
  6. Volume of an ocean:

Units

  • millimeters (mm)
  • feet (ft)
  • meters (m)
  • square inches (sq in)
  • square feet (sq ft)
  • square miles (sq mi)
  • cubic kilometers (cu km)
  • cubic yards (cu yd)
  1. ______________________________: miles
  2. ______________________________: cubic meters

16.2: Building with 8 Cubes

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

GeoGebra Applet uG4wj6fW

For each shape, determine the following information and write it on a sticky note.

  • Give your design a name or a label (e.g., Mae’s First Shape or Eric’s Steps).
  • Determine its volume.
  • Determine its surface area.

16.3: Comparing Prisms Without Building Them

Three rectangular prisms each have a height of 1 cm.

  • Prism A has a base that is 1 cm by 11 cm.
  • Prism B has a base that is 2 cm by 7 cm.
  • Prism C has a base that is 3 cm by 5 cm.

  1. Find the surface area and volume of each prism. Use the dot paper to draw the prisms, if needed.

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

Summary

Length is a one-dimensional attribute of a geometric figure. We measure lengths using units like millimeters, centimeters, meters, kilometers, inches, feet, yards, and miles.

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Area is a two-dimensional attribute. We measure area in square units. For example, a square that is 1 centimeter on each side has an area of 1 square centimeter.

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Volume is a three-dimensional attribute. We measure volume in cubic units. For example, a cube that is 1 kilometer on each side has a volume of 1 cubic kilometer.

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Surface area and volume are different attributes of three-dimensional figures. Surface area is a two-dimensional measure, while volume is a three-dimensional measure.

Two figures can have the same volume but different surface areas. For example:

  • A rectangular prism with side lengths of 1 cm, 2 cm, and 2 cm has a volume of 4 cu cm and a surface area of 16 sq cm.
  • A rectangular prism with side lengths of 1 cm, 1 cm, and 4 cm has the same volume but a surface area of 18 sq cm.
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Similarly, two figures can have the same surface area but different volumes. 

  • A rectangular prism with side lengths of 1 cm, 1 cm, and 5 cm has a surface area of 22 sq cm and a volume of 5 cu cm.
  • A rectangular prism with side lengths of 1 cm, 2 cm, and 3 cm has the same surface area but a volume of 6 cu cm.
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Practice Problems ▶