Question

9 a rectangular tool chest has a length of 6 feet, a width of 3 feet, and a height of 2 feet. emma uses unit cubes, each measuring 1 foot on each side, to pack the tool chest without gaps or overlaps. decide if each statement about the tool chest is true or false. choose true or false for each statement. the area of the base of the chest is 18 square feet. the volume of the chest is 18 cubic feet. emma must use 36 unit cubes to fill the chest. emma must use 2 layers with 9 cubes in each layer to fill the chest. the volume of the chest is 36 cubic feet.

Explanation:

Step1: Calculate base - area

The base of the rectangular tool - chest is a rectangle. The formula for the area of a rectangle is $A = l\times w$, where $l = 6$ feet and $w = 3$ feet. So, $A=6\times3 = 18$ square feet. The first statement is True.

Step2: Calculate volume

The formula for the volume of a rectangular prism is $V=l\times w\times h$. Here, $l = 6$ feet, $w = 3$ feet, and $h = 2$ feet. So, $V=6\times3\times2=36$ cubic feet. The second statement is False.

Step3: Determine number of unit - cubes

Since the volume of the tool - chest is 36 cubic feet and the volume of each unit cube is 1 cubic foot ($1\times1\times1 = 1$ cubic foot), the number of unit cubes needed to fill the chest is 36. The third statement is True.

Step4: Analyze layer and cube number

If we consider layers, if we have 2 layers, and the base - area is 18 square feet. If we want to divide the base - area into equal - sized groups for each layer, if we assume 2 layers, each layer should have 18 unit cubes (not 9). So the fourth statement is False.

Step5: Confirm volume

As calculated in Step 2, the volume of the chest is 36 cubic feet. The fifth statement is True.

Answer:

A. True
B. False
C. True
D. False
E. True