Question

lesson 2
finding volume using unit cubes continued
7
3 ft
6 ft 2 ft
addition:
multiplication:
volume:
8
5 in.
3 in. 3 in.
addition:
multiplication:
volume:

Explanation:

Step1: Understand the volume formula

The volume \(V\) of a rectangular prism is \(V = l\times w\times h\) (where \(l\) is length, \(w\) is width, \(h\) is height). For the addition - based approach (counting unit - cubes layer by layer), we sum up the number of unit - cubes in each layer.

Step2: Solve for problem 7

• Addition:

The base layer has \(6\times2 = 12\) unit - cubes. Since the height \(h = 3\), we have \(12+12 + 12=36\) (summing the number of unit - cubes in 3 layers).

• Multiplication:

Using the formula \(V=l\times w\times h\), with \(l = 6\) ft, \(w = 2\) ft, \(h = 3\) ft. Then \(V=6\times2\times3=36\) \(ft^{3}\)

Step3: Solve for problem 8

• Addition:

The base layer has \(3\times3=9\) unit - cubes. Since the height \(h = 5\), we have \(9 + 9+9+9+9 = 45\) (summing the number of unit - cubes in 5 layers).

• Multiplication:

Using the formula \(V=l\times w\times h\), with \(l = 3\) in, \(w = 3\) in, \(h = 5\) in. Then \(V=3\times3\times5=45\) \(in^{3}\)

Answer:

For problem 7:

• Addition: \(12 + 12+12 = 36\)
• Multiplication: \(6\times2\times3=36\)
• Volume: \(36\space ft^{3}\)

For problem 8:

• Addition: \(9+9 + 9+9+9=45\)
• Multiplication: \(3\times3\times5 = 45\)
• Volume: \(45\space in^{3}\)