Problem Analysis:
The task involves analyzing the given 3D geometric shapes and determining their properties or relationships. The shapes are labeled as (i), (ii), (iii), and (iv). Each shape is constructed using unit cubes, and we need to identify a specific property or pattern among them.
#### Step-by-Step Solution:
1.
Shape (i):
- This is a rectangular prism.
- Dimensions: It appears to be 3 units long, 1 unit wide, and 2 units high.
- Total number of unit cubes: \(3 \times 1 \times 2 = 6\).
2.
Shape (ii):
- This is an L-shaped structure.
- It consists of two parts:
- A vertical column of 3 unit cubes.
- A horizontal row of 2 unit cubes extending from the top of the vertical column.
- Total number of unit cubes: \(3 + 2 = 5\).
3.
Shape (iii):
- This is a T-shaped structure.
- It consists of two parts:
- A vertical column of 3 unit cubes.
- A horizontal row of 2 unit cubes extending from the middle of the vertical column.
- Total number of unit cubes: \(3 + 2 = 5\).
4.
Shape (iv):
- This is a stepped structure.
- It consists of three layers:
- Bottom layer: 3 unit cubes.
- Middle layer: 2 unit cubes.
- Top layer: 1 unit cube.
- Total number of unit cubes: \(3 + 2 + 1 = 6\).
Observations:
-
Shape (i) and Shape (iv) both have 6 unit cubes.
-
Shape (ii) and Shape (iii) both have 5 unit cubes.
- Shapes (ii) and (iii) are similar in structure but differ in orientation:
- Shape (ii) has the horizontal extension at the top of the vertical column.
- Shape (iii) has the horizontal extension in the middle of the vertical column.
Conclusion:
The problem likely asks us to identify a pattern or relationship among the shapes. Based on the observations:
- Shapes (i) and (iv) have the same total number of unit cubes (6).
- Shapes (ii) and (iii) have the same total number of unit cubes (5) but differ in orientation.
If the task is to group the shapes based on the total number of unit cubes:
- Group 1: Shapes (i) and (iv) (6 unit cubes).
- Group 2: Shapes (ii) and (iii) (5 unit cubes).
If the task is to identify a specific property or pattern, the most straightforward answer is the total number of unit cubes.
Final Answer:
\[
\boxed{\text{Shapes (i) and (iv) have 6 unit cubes, while shapes (ii) and (iii) have 5 unit cubes.}}
\]
Parent Tip: Review the logic above to help your child master the concept of isometric drawings worksheet.
