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.
Problem 2
Here is a figure built from snap cubes.
![4 snap cubes forming a rectangular prism, 1 by 1 by 4.](https://cms-im.s3.amazonaws.com/6BtRTBMq8kjwPSxHQbetVAZJ?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP.New.Image.22.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP.New.Image.22.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T010755Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fcb313e6bc91032b362d0dc0a78bb984bff58400ab80edf1e63d5c06c140a7c2)
- Find the volume of the figure in cubic units.
- Find the surface area of the figure in square units.
- 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.”
- Which two figures suggest that her statement is true?
- Which two figures could show that her statement is not true?
![5 figures composed of unit cubes, labeled A, B, C, D, E.](https://cms-im.s3.amazonaws.com/pxZ7pBkxbcrSDz66NpRXs64t?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP.New.Image.21a.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP.New.Image.21a.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T010755Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=626a35403853363fb9c7fae4f7a29149b9c9a7b63ce596f16d54a7da19fb06f9)
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.
Problem 5
-
Draw a net for this rectangular prism.
- Find the surface area of the rectangular prism.