Question

bluebonnet learning k-5 math
lesson 3 homework 5.5
name
date

1. use the prisms to find the volume.

• the rectangular prisms pictured below were constructed with 1 cm cubes.
• decompose each prism into layers in three different ways, and show your thinking on the blank prisms.
• complete each table.

a.

number of layers	number of cubes in each layer	volume of the prism
		cubic cm
		cubic cm

b.

number of layers	number of cubes in each layer	volume of the prism
		cubic cm
		cubic cm

lesson 3: compose and decompose right rectangular prisms using layers.
13

Explanation:

Step1: Analyze first prism (a)

The first rectangular prism has dimensions $4 \text{ cm} \times 2 \text{ cm} \times 2 \text{ cm}$. Volume formula: $V = l \times w \times h$.

Way 1: Layers = 2, cubes per layer

Cubes per layer: $4 \times 2 = 8$
Volume: $2 \times 8 = 16$

Way 2: Layers = 4, cubes per layer

Cubes per layer: $2 \times 2 = 4$
Volume: $4 \times 4 = 16$

Way 3: Layers = 8, cubes per layer

Cubes per layer: $2 \times 1 = 2$
Volume: $8 \times 2 = 16$

Step2: Analyze second prism (b)

The second rectangular prism has dimensions $5 \text{ cm} \times 3 \text{ cm} \times 2 \text{ cm}$.

Way 1: Layers = 2, cubes per layer

Cubes per layer: $5 \times 3 = 15$
Volume: $2 \times 15 = 30$

Way 2: Layers = 3, cubes per layer

Cubes per layer: $5 \times 2 = 10$
Volume: $3 \times 10 = 30$

Way 3: Layers = 5, cubes per layer

Cubes per layer: $3 \times 2 = 6$
Volume: $5 \times 6 = 30$

Answer:

Table a:

Number of Layers	Number of Cubes in Each Layer	Volume of the Prism
4	4	16 cubic cm
8	2	16 cubic cm

Table b:

Number of Layers	Number of Cubes in Each Layer	Volume of the Prism
3	10	30 cubic cm
5	6	30 cubic cm