Question

finding volume using unit cubes
write an addition equation and a multiplication equation to find the volume of each rectangular prism.
1
addition:
multiplication:
volume:
2
addition:
multiplication:
volume:
3
addition:
multiplication:
volume:
4
addition:
multiplication:
volume:
5
addition:
multiplication:
volume:
6
addition:
multiplication:
volume:

Explanation:

Step1: Determine the number of unit cubes in each layer

For a rectangular prism, if the length is \(l\), width is \(w\), and height is \(h\). The number of unit cubes in each layer (based on length and width) is \(l\times w\).

Step2: Use addition (sum of unit - cubes in each layer)

If the height \(h = 2\), and the number of unit - cubes in each layer is \(n\), then the addition equation is \(n + n\). For example, in problem 1: length \(l = 4\) ft, width \(w=2\) ft, height \(h = 2\) ft. The number of unit - cubes in each layer \(n=4\times2 = 8\). The addition equation is \(8+8\).

Step3: Use multiplication (volume formula \(V=l\times w\times h\))

Using the formula \(V = l\times w\times h\). In problem 1: \(l = 4\) ft, \(w = 2\) ft, \(h=2\) ft. Then \(V=4\times2\times2\)

Answer:

1. Addition: \(8 + 8=16\); Multiplication: \(2\times2\times4 = 16\); Volume: \(16\space ft^{3}\)
2. Addition: \(12+12 = 24\) (since \(4\times3=12\) unit - cubes per layer and \(h = 2\)); Multiplication: \(4\times3\times2=24\); Volume: \(24\space cm^{3}\)
3. Addition: \(2+2+2+2=8\) (since \(1\times2 = 2\) unit - cubes per layer and \(h = 4\)); Multiplication: \(1\times2\times4=8\); Volume: \(8\space in^{3}\)
4. Addition: \(4 + 4+4=12\) (since \(2\times2=4\) unit - cubes per layer and \(h = 3\)); Multiplication: \(2\times2\times3=12\); Volume: \(12\space ft^{3}\)
5. Addition: \(9+9=18\) (since \(3\times3 = 9\) unit - cubes per layer and \(h = 2\)); Multiplication: \(2\times3\times3=18\); Volume: \(18\space cm^{3}\)
6. Addition: \(10+10+10+10=40\) (since \(5\times2=10\) unit - cubes per layer and \(h = 4\)); Multiplication: \(2\times5\times4=40\); Volume: \(40\space cm^{3}\)