# Spatial Relations – Blocks and Touching Blocks

- Posted by Brian Stocker
- Date June 28, 2023
- Comments 3 comments

### Blocks and Touching Blocks Practice

**Touching Blocks **

Touching Blocks questions give a complex image of blocks and you are asked to count the number of blocks a given block is touching.

**Blocks – Cubes**

Blocks questions present a complex geometric figure made of a series of rectangular or square blocks. You are asked the number of blocks in the figure.

### Touching Blocks

**1. How many blocks is block A touching?**

a. 4

b. 5

c. 6

d. 7

**2. How many blocks is block B touching?**

a. 4

b. 5

c. 9

d. 10

**3. How many blocks is block C touching?**

a. 4

b. 3

c. 2

d. 1

### Blocks (Cubes)

**1. How many cubes are there in the figure?**

a. 30

b. 32

c. 35

d. 24

**2. How many cubes are there in the figure?**

a. 30

b. 22

c. 15

d. 24

**3. How many cubes must we add in the figure to form a perfect cube?**

a. 55

b. 45

c. 70

d. 125

### Answer Key

**Touching Blocks**

**1. C**

Block A touches 6 blocks (1 is below, 4 are lateral in vertical position and 1 is lateral in the horizontal position.

**2. D**

Block B touches 5 blocks below, 4 blocks above and one block laterally, i.e. in total 10 blocks.

**3. A**

Block C touches 4 blocks in total: 1 below, 2 blocks laterally on the wider side and one block laterally, in the narrower side.

**Blocks**

**1. C**

In the bottom row, there are 3 × 4 + 3 = 15 cubes.

In the next row, there are 2 + 3 + 3 + 3 + 1 = 12 cubes.

In the third row, there are 2 + 2 = 4 cubes.

In the upper row, there are only 2 cubes.

Thus, in total there are 15 + 12 + 4 + 2 = 33 cubes.

**2. D**

From the figure, you will see that there are 4 + 4 + 2 + 3 + 3

= 16 cubes in the bottom row, 2 + 1 + 2 + 1 = 6 cubes in the

middle row and only 2 cubes in the upper row.

Thus, in total there are 16 + 6 + 2 = 24 cubes in the figure.

**3. C**

Since there are 5 cubes in the longest row, we need 5 × 5 × 5 = 125 cubes in total to form a perfect cube.

First, let’s count the existing cubes. In the first row, there are 5 + 4 + 5 + 5 + 4 = 23 cubes.

In the second row, there are 5 + 3 + 4 + 4 + 1 = 17 cubes.

In the third row, there are 3 + 3 + 2 = 8 cubes.

In the fourth row, there are 3 + 3 + 1 = 7 cubes.

Thus, in total there are 23 + 17 + 8 + 7 = 55 cubes.

Hence, we must add 125 – 55 = 70 cubes to form a perfect big cube.

**Written by**, Brian Stocker MA., Complete Test Preparation Inc.

**Date Published:**Wednesday, June 28th, 2023

**Date Modified:**Saturday, October 14th, 2023

Got a Question? Email me anytime - Brian@test-preparation.ca

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## 3 Comments

Can you show the solution diagram for the cubes questions we I can visualize?

3. How many cubes must we add in the figure to form a perfect cube?

The correct answer is 36! Review and fix the issue!

The question is correct. Take the total number of cubes for a complete cube (5 X 5 X 5 = 125) and subtract the number of cubes in the figure (55) to get the number of cubes to make a complete cube.

So 125 – 55 = 70