Lesson 11
Squares and Cubes
Let’s investigate perfect squares and perfect cubes.
Problem 1
What is the volume of this cube?
![cube, side length = 2 centimeters](https://staging-cms-im.s3.amazonaws.com/wuFh2WDwbsqEFPgUaGCTbu8W?response-content-disposition=inline%3B%20filename%3D%226-6.1.F.PP_Image_1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.F.PP_Image_1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T075411Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5bcb5d96b369f8fdf65d23785d240aa41483d701f8c650b139a28655d7be222d)
Problem 2
-
Decide if each number on the list is a perfect square.
16
20
25
100
125
144
225
10,000
- Write a sentence that explains your reasoning.
Problem 3
-
Decide if each number on the list is a perfect cube.
1
3
8
9
27
64
100
125
- Explain what a perfect cube is.
Problem 4
-
A square has side length 4 cm. What is its area?
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The area of a square is 49 m2. What is its side length?
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A cube has edge length 3 in. What is its volume?
Problem 5
Prism A and Prism B are rectangular prisms.
- Prism A is 3 inches by 2 inches by 1 inch.
- Prism B is 1 inch by 1 inch by 6 inches.
Select all statements that are true about the two prisms.
They have the same volume.
They have the same number of faces.
More inch cubes can be packed into Prism A than into Prism B.
The two prisms have the same surface area.
The surface area of Prism B is greater than that of Prism A.
Problem 6
-
What polyhedron can be assembled from this net?
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What information would you need to find its surface area? Be specific, and label the diagram as needed.
Problem 7
Find the surface area of this triangular prism. All measurements are in meters.
![trianglular prism with dimensions provided](https://staging-cms-im.s3.amazonaws.com/MPkEH7foGoYma7jqj4A3w54y?response-content-disposition=inline%3B%20filename%3D%226-6.1.E4_Image_3.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E4_Image_3.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T075411Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ea0a2d028d7684af08ad534611630d3ce8c54c9cc8c68d75d47b0eb7e769075d)