A right square prism has a volume of 360 cubic units.
Which could be the dimensions, in units, of the prism? Select three options.

A. 3 by 3 by 40
B. 4 by 4 by 20
C. 5 by 5 by 14
D. 25 by 12 by 12
E. 3.6 by 10 by 10



Answer :

To determine which sets of dimensions could be that of a right square prism with a volume of 360 cubic units, we need to verify that the volume of each given prism matches 360 cubic units. The volume [tex]\( V \)[/tex] of a right square prism is calculated as:

[tex]\[ V = \text{length} \times \text{width} \times \text{height} \][/tex]

Given the five options, let's verify each one:

1. Dimensions: 3 by 3 by 40
[tex]\[ V = 3 \times 3 \times 40 = 9 \times 40 = 360 \, \text{cubic units} \][/tex]
These dimensions are valid since the volume is 360 cubic units.

2. Dimensions: 4 by 4 by 20
[tex]\[ V = 4 \times 4 \times 20 = 16 \times 20 = 320 \, \text{cubic units} \][/tex]
These dimensions are not valid since the volume is 320 cubic units.

3. Dimensions: 5 by 5 by 14
[tex]\[ V = 5 \times 5 \times 14 = 25 \times 14 = 350 \, \text{cubic units} \][/tex]
These dimensions are not valid since the volume is 350 cubic units.

4. Dimensions: 25 by 12 by 12
[tex]\[ V = 25 \times 12 \times 12 = 300 \times 12 = 3600 \, \text{cubic units} \][/tex]
These dimensions are not valid since the volume is 3600 cubic units.

5. Dimensions: 3.6 by 10 by 10
[tex]\[ V = 3.6 \times 10 \times 10 = 36 \times 10 = 360 \, \text{cubic units} \][/tex]
These dimensions are also valid since the volume is 360 cubic units.

Hence, the valid sets of dimensions that give a volume of 360 cubic units are:

1. 3 by 3 by 40
2. 3.6 by 10 by 10