Question

directions: type your response in the box. 5 mrs. jones asked her students to fully pack this rectangular prism with unit cubes. it will take layers of unit cubes to fill the prism. julia said, \the volume of the rectangular prism is 45 cubic units.\ anna said, \the volume of the rectangular prism is 60 cubic units\ part a: which student gave the correct volume of the rectangular prism? show one method the student may have used to find the correct volume. part b: explain a possible mistake made by the student who gave the incorrect volume. rubric response: score: /2

Explanation:

Step1: Count base - layer cubes

Count the number of unit - cubes in the base layer. There are 3 rows and 4 columns of unit - cubes in the base layer, so the number of unit - cubes in the base layer is $3\times4 = 12$.

Step2: Determine number of layers

We are told that it takes 5 layers of unit - cubes to fill the prism.

Step3: Calculate volume

The volume $V$ of a rectangular prism is given by the formula $V=\text{(number of unit - cubes in base layer)}\times\text{(number of layers)}$. So $V = 12\times5=60$ cubic units.

Answer:

Part A: Anna gave the correct volume. One method to find the volume is to first count the number of unit - cubes in the base layer (3 rows and 4 columns, so 12 unit - cubes) and then multiply by the number of layers (5), resulting in $12\times5 = 60$ cubic units.
Part B: Julia may have made a mistake by either miscounting the number of unit - cubes in the base layer or the number of layers. For example, if she thought there were 3 rows and 3 columns in the base layer (9 unit - cubes) and multiplied by 5 layers, she would get $9\times5 = 45$ cubic units.