# Cubes and Dices practice test

1.

Choose the box that is similar to the box formed from the given sheet of paper (X).

Answer: Option D

Explanation:

The fig. (X) is similar to the Form V. So, when the sheet in fig. (X) is folded to form a cube, then the face bearing a dot appears opposite to a blank face, the face bearing a ‘+’ sign appears opposite to another blank face and the face bearing a circle appears opposite to the third blank face. Clearly, all the four cubes shown in figures (1), (2), (3) and (4) can be formed.

2.

A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining, while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up.

How many cubes have only one coloured face each ?

Answer: Option C

Explanation:

8 from (I) and 8 from (II)

Therefore 8 from each.

3.

A dice is numbered from 1 to 6 in different ways.

If 1 is opposite to 5 and 2 is opposite to 3, then

Answer: Option B

Explanation:

If 1 is opposite to 5 and 2 is opposite to 3, then 4 definitely lies opposite to 6. Therefore, 2 cannot lie opposite to any of the two numbers – 4 or 6. Hence, 2 necessarily lies adjacent to both 4 and 6.

4.

Directions (Q. Nos 4-8) Read the following informaion and answer the questions that follow:

A wooden cube of side 4cm has been painted with different colours. The two opposite srfaces are painted red, the other two with green colour. Out of the remaining two surfaces, one is painted white and the other is painted black. Now the cube is cut into 64 equal cubes.

How many cubes have only green colour?

Answer: Option D

Explanation:

Total cubes 4x4x4 =64

only green =8       Red/green/white=4      Green and black =4

only white =4       Red/green/black=4      Green and white=4

only Red =8         Red and black=4         Green and red=8

only Balck =4       Red and white=4         No colour=8

5.

How many cubes have three colours red, green and white?

Answer: Option B
6.

How many cubes have only two colours, red and black?

Answer: Option A
7.

How many cubes have only black colour?

Answer: Option C
8.

How many cubes do not have any coloured face?

Answer: Option B
9.

Two positions of a dice are shown below: When 2 is at the bottom, what number will be at the top?

Answer: Option C

Explanation:

Number 3 is common to both the figures (i) and (ii). The dice in fig. (ii) is assumed to be rotated so that 3 remains on the FR-RH face (i.e. face I as per activity 1) and the numbers 5 and 2 move to the faces hidden behind the numbers 6 and 1 respectively [in fig. (i)]. Thus, the combined figure will have 3 on FR-RH face (i.e. face I), 5 on RR-RH face (i.e. face II), 2 on Bottom face (i.e. face VI), 1 on the Top face (i.e. face V) and 6 on FR-LH face (i.e. face IV). Clearly, 2 lies opposite 1. Hence, when 2 is at the bottom, then 1 will be at the top.

10.

A 4 cm cube is cut into 1 cm cubes. The total surface area of all the small cubes is :

Answer: Option C

Explanation:

Number of cubes = (Volume of bigger cube)/(Volume of smaller cube)

= [(4*4*4)/(1*1*1)]= 64
Surface area of all small cubes = 64*[6*(1)2] = 384 cm2.