Spatial Relations – Blocks and 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

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

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.