Let's solve each part of the problem step by step.
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Part 1: Rectangular Prisms Built from Centimeter Cubes
We are given two prisms made up of unit cubes (each cube is 1 cm × 1 cm × 1 cm). We need to determine the
length,
width,
height, and
volume of each prism.
---
####
a. First Prism
Looking at the image:
- The base has
6 cubes in a row →
Length = 6 cm
- The depth (going into the page) has
2 cubes →
Width = 2 cm
- The height has
2 layers →
Height = 2 cm
Now calculate the
volume:
$$
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = 6 \times 2 \times 2 = 24 \text{ cm}^3
$$
✔ So:
- Length:
6 cm
- Width:
2 cm
- Height:
2 cm
- Volume:
24 cm³
---
####
b. Second Prism
This one is a cube-like structure:
- Front face shows
3 rows high →
Height = 3 cm
- Each row has
3 cubes wide →
Width = 3 cm
- Depth (into the page):
2 cubes →
Length = 2 cm
Wait — let’s double-check orientation.
Actually, based on standard labeling:
-
Length = number of cubes along the longest side (horizontal)
-
Width = depth (side-to-side)
-
Height = vertical
But since it's a stack of cubes, we can count:
- There are
3 columns in width (front view)
-
3 layers in height
-
2 cubes deep (back-to-front)
So:
-
Length: 3 cm (horizontal front edge)
-
Width: 2 cm (depth)
-
Height: 3 cm (vertical)
Wait — actually, let’s look carefully.
The figure shows:
- 3 cubes across the front (left to right) →
Length = 3 cm
- 2 cubes back to front (depth) →
Width = 2 cm
- 3 cubes tall →
Height = 3 cm
So:
- Length:
3 cm
- Width:
2 cm
- Height:
3 cm
$$
\text{Volume} = 3 \times 2 \times 3 = 18 \text{ cm}^3
$$
✔ So:
- Length:
3 cm
- Width:
2 cm
- Height:
3 cm
- Volume:
18 cm³
---
Part 2: Calculate Volume with Given Dimensions
Use the formula:
$$
V = \text{Length} \times \text{Width} \times \text{Height}
$$
---
####
a. Cube with dimensions: 4 in × 3 in × 4 in
Note: It's not a perfect cube, just a rectangular prism.
- Length = 4 in
- Width = 3 in
- Height = 4 in
$$
V = 4 \times 3 \times 4 = 48 \text{ in}^3
$$
✔ V = 48 in³
---
####
b. Prism with dimensions: 3 m × 2 m × 6 m
- Length = 3 m
- Width = 2 m
- Height = 6 m
$$
V = 3 \times 2 \times 6 = 36 \text{ m}^3
$$
✔ V = 36 m³
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✔ Final Answers:
---
Part 1:
a.
- Length:
6 cm
- Width:
2 cm
- Height:
2 cm
- Volume:
24 cm³
b.
- Length:
3 cm
- Width:
2 cm
- Height:
3 cm
- Volume:
18 cm³
---
Part 2:
a.
$ V = 4 \times 3 \times 4 = \boxed{48} $
in³
b.
$ V = 3 \times 2 \times 6 = \boxed{36} $
m³
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Let me know if you'd like a visual explanation or help understanding how to count cubes!
Parent Tip: Review the logic above to help your child master the concept of volume of composite rectangular prisms worksheet.
