Section A Section A Checkpoint

Problem 1

Which figure has greater volume? Explain your reasoning.

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Solution

A. Sample response: Figure A is 10 unit cubes and Figure B is only 9 unit cubes, so Figure A takes up more space.

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Sample Response

A. Sample response: Figure A is 10 unit cubes and Figure B is only 9 unit cubes, so Figure A takes up more space.

Problem 2

Find the volume of each prism. Explain or show your reasoning.

Rectangular prism. 5 cubes by 3 cubes by 2 cubes. — a.

Rectangular prism partially filled. Base, 5 cubes by 4 cubes. Height shown as 3 cubes. — b.

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Solution

30 unit cubes (or equivalent). Sample response: There are 2 layers of 15 cubes.
60 unit cubes (or equivalent). Sample response: The base layer has 20 cubes and there are 3 layers in the full prism.

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Sample Response

30 unit cubes (or equivalent). Sample response: There are 2 layers of 15 cubes.
60 unit cubes (or equivalent). Sample response: The base layer has 20 cubes and there are 3 layers in the full prism.

Problem 3

Explain or show how the expression $4 \times 6$ represents the volume of the rectangular prism in cubes.

Rectangular prism. 2 cubes by 3 cubes by 4 cubes.

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Solution

Sample response: The layer of cubes the prism sits on has 6 cubes. There are 4 of these layers in the prism. So the volume is $4 \times 6$ unit cubes.

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Sample Response

Sample response: The layer of cubes the prism sits on has 6 cubes. There are 4 of these layers in the prism. So the volume is $4 \times 6$ unit cubes.