Lesson 16

Distinguishing Between Surface Area and Volume

Let’s contrast surface area and volume.

Problem 1

Match each quantity with an appropriate unit of measurement.

A:

The surface area of a tissue box

B:

The amount of soil in a planter box

C:

The area of a parking lot

D:

The length of a soccer field

E:

The volume of a fish tank

1:

Square meters

2:

Yards

3:

Cubic inches

4:

Cubic feet

5:

Square centimeters

Problem 2

Here is a figure built from snap cubes.

4 snap cubes forming a rectangular prism, 1 by 1 by 4.
  1. Find the volume of the figure in cubic units.
  2. Find the surface area of the figure in square units.
  3. True or false: If we double the number of cubes being stacked, both the volume and surface area will double. Explain or show how you know.

Problem 3

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

  1. Which two figures suggest that her statement is true?
  2. Which two figures could show that her statement is not true?
5 figures composed of unit cubes, labeled A, B, C, D, E.

Problem 4

Draw a pentagon (five-sided polygon) that has an area of 32 square units. Label all relevant sides or segments with their measurements, and show that the area is 32 square units.

(From Unit 1, Lesson 11.)

Problem 5

  1. Draw a net for this rectangular prism.

    2 by 5 by 10 centimeter rectangular prism.

  2. Find the surface area of the rectangular prism.
(From Unit 1, Lesson 15.)