Question

The following questions are based on the information given below:

1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.

2. Two faces measuring 4 cm x 1 cm are coloured in black.

3. Two faces measuring 6 cm x 1 cm are coloured in red.

4. Two faces measuring 6 cm x 4 cm are coloured in green.

5. The block is divided into 6 equal cubes of side 1 cm (from 6 cm side), 4 equal

cubes of side 1 cm (from 4 cm side).

Questions:

1.

1. How many cubes having red, green and black colours on atleast one side of

the cube will be formed?

2. How many small cubes will be formed?

3. How many cubes will have 4 coloured sides and two non – coloured sides?

4. How many cubes will have green colour on two sides and rest of the four

sides having no colour?

5. How many cubes will remain if the cubes having black and green coloured

are removed?​

Answer 1

Cube and Cuboids- logical reasoning  

Given:

A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.

Two faces measuring 4 cm x 1 cm are colored in black.

Two faces measuring 6 cm x 1 cm are colored in red.

Two faces measuring 6 cm x 4 cm are colored in green.

To find:

Number of cubes having red, black and green color on at least one side.

Number of small cubes formed.

Number of cubes having 4 side colored and 2 non-colored side.

Number of cubes having green color on 2 sides and other sides don't have any color.

Number of cubes remain if black and green colored are removed.

Explanation:

A picture showing the cuboid is attached for easy visualization.

1. The cubes having red, green and black color cubes are related to the corners of the cuboid. So, the number of corners of the cuboid is 4. Hence, the number of such small cubes is 4.
2. Number of small cubes will be $(6\times4\times1)=24\ cubes.$
3. Only 4 cubes which will be situated at the corners of the cuboid will have 4 colored sides and 2 non-colored sides.
4. There are 16 small cubes attached to the outer part of the cuboid. Hence the cubes left will have two green colored wall and 4 walls having no color on it. So, the number of such cubes will be $(24-16)=8 \ cubes$.
5. Number of remaining cubes will be equal to the difference of total number of cubes and number of cubes which are black and green. Black and green colored cubes are 8 in number. So, required number of such cubes will be $(24-8)=16$ .