# PE 1 - Cubes | LR - Cubes

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**Answer the following questions based on the information given below.**

A cuboid shaped wooden block has 10 cm length, 5 cm breadth and 1 cm height.

- Two faces measuring 10 cm × 5 cm are colored in blue.
- Two faces measuring 10 cm × 1 cm are colored in red.
- Two faces measuring 5 cm × 1 cm are colored in green.

The block is divided into 10 equal cubes of side 1 cm (from 10 cm side), 5 equal cubes of side 1 cm (from 5 cm side).

**PE 1 - Cubes | LR - Cubes**

How many cubes having red, green and blue colors on at least one side of the cube will be formed?

- (a)
16

- (b)
12

- (c)
10

- (d)
4

Answer: Option D

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**Explanation** :

Such cubes are related to the corners of the cuboid. Since the number of corners of the cuboid is 4.

Hence, the number of such small cubes is 4.

Hence, option (d).

Workspace:

**PE 1 - Cubes | LR - Cubes**

How many small cubes will be formed?

Answer: 50

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**Explanation** :

Number of small cubes = l × b × h = 10 × 5 × 1 = 50

Hence, 50.

Workspace:

**PE 1 - Cubes | LR - Cubes**

How many cubes will have 4 colored sides and two non-colored sides?

- (a)
8

- (b)
4

- (c)
16

- (d)
10

Answer: Option B

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**Explanation** :

Only 4 cubes situated at the corners of the cuboid will have 4 colored and 2 non-colored sides.

Hence, option (b).

Workspace:

**PE 1 - Cubes | LR - Cubes**

How many cubes will have blue color on two sides and rest of the four sides having no color?

- (a)
24

- (b)
0

- (c)
32

- (d)
26

Answer: Option A

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**Explanation** :

There are 24 small cubes attached to the outer walls of the cuboid.

Therefore, remaining inner small cubes will be the cubes having two sides blue colored.

So, the required number = 50 - 26 = 24

Hence, option (a).

Workspace:

**PE 1 - Cubes | LR - Cubes**

How many cubes will remain if the cubes having blue and green colored are removed?

Answer: 40

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**Explanation** :

Number of small cubes which are blue and green is 10 in all (5 each from two edges).

Hence, the number of remaining cubes = 50 - 10 = 40

Hence, 40.

Workspace:

Answer the following questions based on the information given below.

There is a cuboid whose dimensions are 3 × 4 × 5 cm.

- The opposite faces of dimensions 3 × 4 are colored yellow.
- The opposite faces of other dimensions 4 × 5 are colored red.
- The opposite faces of dimensions 5 × 3 are colored blue.

Now the cuboid is cut into smaller cubes of side 1 cm.

**PE 1 - Cubes | LR - Cubes**

How many small cubes have three faces colored?

- (a)
24

- (b)
20

- (c)
16

- (d)
8

Answer: Option D

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**Explanation** :

Such cubes are related to the corners of the cuboid and in this cuboid there are 8 corners.

Hence, the required number of small cubes is 8.

Hence, option (d).

Workspace:

**PE 1 - Cubes | LR - Cubes**

How many smaller cubes will have only two faces colored?

- (a)
12

- (b)
24

- (c)
16

- (d)
12

Answer: Option B

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**Explanation** :

Exactly two faces colored will come from edges.

4 edges of blue and red with 3 cubes from each edge, i.e., total 4 × 3 = 12 cubes.

4 edges of red and yellow with 1 cube from each edge, i.e., total 4 × 1 = 4 cubes.

4 edges of yellow and blue with 2 cubes from each edge, i.e., total 4 × 2 = 8 cubes.

∴ Total = 12 + 4 + 8 = 24 cubes will have exactly two faces colored.

Hence, option (b).

Workspace:

**PE 1 - Cubes | LR - Cubes**

How many small cubes will have only one face colored?

- (a)
20

- (b)
22

- (c)
24

- (d)
28

Answer: Option B

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**Explanation** :

2 blue faces will give 6 such cubes each i.e., 12 cubes.

2 red faces will give 3 such cubes each i.e., 6 cubes.

2 yellow faces will give 2 such cubes each i.e., 4 cubes.

∴ Total 12 + 6 + 4 = 22 cubes will have exactly one face colored.

Hence, option (b).

Workspace:

**PE 1 - Cubes | LR - Cubes**

How many small cubes will have no face colored?

- (a)
1

- (b)
2

- (c)
4

- (d)
6

Answer: Option D

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**Explanation** :

Required number of small cubes = (3 - 2) × (4 - 2) × (5 - 2) = 1 × 2 × 3 = 6

Hence, option (d).

Workspace:

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