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6th grade

Course: 6th grade > Unit 10

Lesson 5: Surface area
Math
6th grade
3D figures
Surface area
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Surface area versus volume

Google Classroom
A 3D figure has both surface area and volume measurements, but we use them for different purposes. Learn the difference and when to use each.

Making sense of units

We have many types of units. Some measure length in 1 dimension. Some measure area in 2 dimensions. Others measure volume in 3 dimensions. Units come in larger and smaller sizes, too.
1.1
For each quantity, choose the most appropriate unit of the choices.
1

Key measurement terms

Length is a 1-dimensional measurement. It tells us the number of units between one point and another. We measure length in units like centimeters, inches, feet, meters, kilometers, and miles.
  • Perimeter is a special example of length. It is the distance around a closed 2D figure.
Area is a 2-dimensional measurement. It tells us the amount of space enclosed in a 2D figure. We measure area in square units such as square centimeters (cm2), square inches, and square meters.
  • Surface area is a special example of area. It tells us the number of square units it would take to cover the faces of the 3D figure.
Volume is a 3-dimensional measurement. It tells us the number of cubic units it would take to fill a 3D figure. We measure volume in units like cubic centimeters (cm3), cubic inches, and cubic meters. For liquids, we sometimes use different volume units, such as milliliters, cups, liters, and gallons.
Notice, this means that we can measure both the surface area and the volume of a 3D figure, but they tell us different things about the figure.

Distinguishing area and volume

Let's consider the same situations from before, this time to decide whether which type of measurement makes the most sense.
2.1
Decide whether we would use area, volume, or neither in each context.
ContextMeasurement
Thickness of a pencil lead
Amount of water in the ocean
Distance around a bathroom
Space covered by a stamp
Room inside a closet
Space painted on a table

The same 3D figure can have both surface area and volume.
Let's contrast the volume and surface area of two figures.
3.1
Answer 2 questions about the following figure.
  1. What is the volume of the figure?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
cubic units
  1. What is the surface area of the figure?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
square units

3.2
Answer 2 questions about the following figure.
  1. What is the volume of the figure?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
cubic units
  1. What is the surface area of the figure?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
square units

So the figures have the same volume, but different surface areas!
The opposite is possible, too. Two figures could have the same surface area, but different volumes.

Try it out!

4.1
The following figure shows a right rectangular prism.
What is the volume of the prism?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
cm3

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