Unit 1, Lesson 16
Distinguishing Between Surface Area and Volume
Grade 6
16.3
Activity
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.
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Find the surface area and volume of each prism. Use the dot paper to draw the prisms, if needed.
- Analyze the volumes and surface areas of the prisms. What do you notice? Write 1 or 2 observations about them.
Student Lesson 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.
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.
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.
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.
On left, rectangular prism with side lengths of 1 centimeter, 2 centimeters, and 2 centimeters has a volume of 4 cubic centimeters and a surface area of 16 square centimeters. On right, rectangular prism with side lengths of 1 centimeter, 1 centimeter, and 4 centimeters has the same volume but a surface area of 18 square centimeters.
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.
On left, rectangular prism with side lengths of 1 centimeter, 1 centimeter, and 5 centimeters has a surface area of 22 square centimeters and a volume of 5 cubic centimeters. On right, rectangular prism with side lengths of 1 centimeter, 2 centimeters, and 3 centimeters has the same surface area but a volume of 6 cubic centimeters.
Volume is the number of cubic units that fill a three-dimensional region with no gaps or overlaps.
This rectangular prism has 3 layers that are each 20 units3. So, the volume of the prism is 60 units3.