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Creative 3D block designs on a grid background.

A colorful arrangement of 3D block structures on a dotted grid, including green, red, blue, yellow, and pink cubes forming various shapes and patterns.

A colorful arrangement of 3D block structures on a dotted grid, including green, red, blue, yellow, and pink cubes forming various shapes and patterns.

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Show Answer Key & Explanations Step-by-step solution for: Isometric Drawing and 3D Cubes | Passys World of Mathematics

Problem Description:


The image shows a collection of 3D block structures made up of smaller cubes. The task is to determine the total number of small cubes used in each structure and then solve any related problem or question based on the given context.

Step-by-Step Solution:



#### 1. Count the Number of Cubes in Each Structure:

##### Top Left Structure (Green):
- This is a 3x3 square with a hollow center.
- Total cubes in a solid 3x3 square: \(3 \times 3 = 9\).
- The hollow center removes 1 cube.
- Total cubes: \(9 - 1 = 8\).

##### Top Right Structure (Red and Yellow):
- There are 3 red cubes in a row.
- There is 1 yellow cube above the rightmost red cube.
- Total cubes: \(3 + 1 = 4\).

##### Middle Right Structure (Blue, Cyan, and Yellow):
- Bottom layer: 3 yellow cubes in a row.
- Middle layer: 2 cyan cubes (one above the left yellow cube and one above the middle yellow cube).
- Top layer: 1 blue cube above the right cyan cube.
- Total cubes: \(3 + 2 + 1 = 6\).

##### Bottom Left Structure (Pink and Cyan):
- Bottom layer: 1 cyan cube.
- Middle layer: 1 pink cube above the cyan cube.
- Top layer: 2 pink cubes side by side above the middle layer.
- Total cubes: \(1 + 1 + 2 = 4\).

##### Bottom Middle Structure (Blue):
- This is a single blue cube.
- Total cubes: \(1\).

##### Bottom Right Structure (Blue):
- This is a 2x2 square of blue cubes.
- Total cubes: \(2 \times 2 = 4\).

#### 2. Summarize the Total Number of Cubes for Each Structure:

- Top Left (Green): 8 cubes
- Top Right (Red and Yellow): 4 cubes
- Middle Right (Blue, Cyan, and Yellow): 6 cubes
- Bottom Left (Pink and Cyan): 4 cubes
- Bottom Middle (Blue): 1 cube
- Bottom Right (Blue): 4 cubes

#### 3. Calculate the Total Number of Cubes in All Structures:
\[
8 + 4 + 6 + 4 + 1 + 4 = 27
\]

Final Answer:


\[
\boxed{27}
\]
Parent Tip: Review the logic above to help your child master the concept of isometric drawings worksheet.
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