# Cubes

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Directions: In the following questions,certain information regarding cubes are given on the basis of which you need to select the best option. You can also review your choices by clicking into answer section.

1. A cube of side 12cm is painted with 3 colors, red, blue and green such that the opposite faces have the same color. It is then cut into 216 equal smaller cubes. What is the side of a smaller cube?

a) 3 cm

b) 2 cm

c) 8 cm

d) 6 cm

Ans: Option B

Explanation:

Volume of a smaller cube = (12*12*12)/216 = 8cm³

Side of a smaller cube = 2cm

2. The following questions are based on the information given below:

1. All the faces of cubes are painted with red color.

2. The cubes are cut into 64 equal small cubes.

I. How many small cubes have only one face coloured?

A. 4

B. 8

C. 16

D. 24

Ans: Option D

Explanation:

Number of small cubes having only one face coloured = (x – 2)2 x No. of faces

= (4 – 2)2 x 6

= 24

II. How many small cubes have no faces coloured?

A. 24

B. 8

C. 16

D. 0

Ans: Option B

Explanation:

Number of small cubes having only one faces coloured = (x – 2)3

Here, x = side of big cube / side of small cube

x = 4 /1

x = 4

Required number = (4 -2)3

= 8

III. How many small cubes are there whose three faces are coloured?

A. 4

B. 8

C. 16

D. 24

Ans: Option B

Explanation:

Number of small cubes having three faces coloured

= No. of corners = 8

IV. How many small cubes are there whose two adjacent faces are coloured red?

A. 0

B. 8

C. 16

D.24

Ans: Option D

Explanation:

Number of small cubes having two adjacent faces coloured red

= (x – 2) x No. of edges

= (4 – 2) x 12

= 24

3. A cube is coloured orange on one face, pink on the opposite face , brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. How many cubes have at least one face coloured pink?

A. 1

B. 9

C. 16

D. 25

Ans: Option D

Explanation:

Each face has n² = 25 cubes.

The 25 cubes on the pink face have atleast one face coloured pink.

4. 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.

I. How many cubes have only one coloured face each?

A.32

B.8

C.16

D.0

Ans: Option C

Explanation:

8 from (I) and 8 from (II)

Therefore, 8 from each.

II. What is the number of cubes with at least one green face each ?

A. 36

B. 32

C. 38

D. 48

Ans: Option C

Explanation:

24 from (I) and 14 from (II)

III. How many cubes have two red and one green face on each ?

A. 0

B. 8

C. 16

D. 4

Ans: Option D

Explanation:

None from (I) and 4 from (II)

IV. How many cubes have no coloured face at all ?

A. 32

B. 8

C. 16

D. None

Ans: Option D

Explanation:

There is no such cube in all, where all the faces are unclosured.

V. How many cubes have each one red and another green?

A. 0

B. 8

C. 16

D. 24

Ans: Option D

Explanation:

16 from (I) and 8 from (II)

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