Dice Test

Result

Dice Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

A cube is painted yellow on all sides. It is then cut into 64 smaller cubes of equal size. How many of these smaller cubes are painted on only one side?

A
4

B
8

C
16

D
24

Solution

The 4 central cubes on each of the 6 faces of the cube, i.e. 24 cubes, will have only one side painted.
Question 2
1 / -0

Directions: The following figures show the same die in different orientations.

How many dots are there on the face opposite to the face having four dots?

A
3

B
2

C
5

D
6

E
None of these

Solution

If two faces in two orientations of the same die are the same, then the remaining faces are opposite to each other.
Since 1 dot and 5 dots are common in both the orientations, so 2 dots are on the face opposite to the face having 4 dots.
Question 3
1 / -0

Directions: Study the following information carefully and answer the question that follows.

A cube having a volume of 216 cm³ is painted red on two opposite sides, black on the other two opposite sides and green on the remaining two opposite sides. It is then cut into cubes with sides of 1 cm each.

How many cubes have no sides painted?

A
8

B
64

C
16

D
24

Solution

Volume of a cube = (Side)³ = 216 cm³
Side = 6 cm
Number of small cubes that will have no sides painted = (x - 2)³
Here, x = (6/1) = 6
So, number of small cubes that will have no sides painted = (6 - 2)³ = 4³ = 64
Question 4
1 / -0

A cube having volume 216 cm³ is painted red on two opposite faces, black on another two opposite faces and green on the remaining two opposite faces. It is then cut into smaller cubes with each side measuring 1 cm.

How many of the smaller cubes have just one painted face?

A
96

B
106

C
36

D
92

Solution

There will be 36 cubes on each face of the larger cube, from which the middle 4 x 4 slot will not be common to any other face and hence, those smaller cubes will have only one painted face.
Number of smaller cubes on each face of the bigger cube having just one painted face = 4 x 4 = 16
Total number of smaller cubes on all six faces of the bigger cube having just one painted face = 16 x 6 = 96
Question 5
1 / -0

Directions: Read the information given below and answer the question that follows.

A cube having volume 216 cm³ is painted red on two opposite sides, black on other two opposite sides and green on the remaining two opposite sides. It is then cut into cubes with each side measuring 1 cm.

How many cubes have three faces painted?

A
4

B
10

C
8

D
9

Solution

The cube having volume 216 cm³ is divided into 216 smaller cubes each of side 1 cm.
The main cube having all the faces painted has smaller cubes with three faces painted at the corners.
Therefore, 8 corner cubes will have 3 faces painted.
Question 6
1 / -0

Directions: Read the following information and answer the question that follows.

A cube having volume 216 cm³ is painted red on two opposite sides, black on other two opposite sides and green on the remaining two opposite sides. It is then cut into cubes, each of edge length 1 cm.

How many cubes have only two or three sides painted?

A
96

B
64

C
56

D
108

Solution

Total number of cubes, each of edge length 1 cm = 216
Now, cubes with two or three sides painted = Cubes at the corners and cubes along the edges
Required number of cubes = 8 (Cubes at the corners) + 48 (4 along each of the 12 edges) = 56 cubes.
Question 7
1 / -0

Directions: Read the following information and answer the question that follows.

A cube having a volume of 216 cm³ is painted red on two opposite sides, black on other two opposite sides and green on the remaining two opposite sides. It is then cut into cubes, each of edge length 1 cm.

How many cubes have one side painted black and the other sides unpainted?

A
16

B
32

C
64

D
6

Solution

The cubes with one side painted black are the cubes on the faces painted black, but not along the edges.
The number of cubes on a face not touching the edges = 4 × 4 = 16
Thus, number of cubes with one side painted black = 16 cubes on each of the two faces painted black = 32 cubes
Question 8
1 / -0

On a dice, a, b, c and d are written on the adjacent faces in a clockwise order, and e and f are written at the top and the bottom of the cube, respectively. What will be at the bottom when c is at the top?

A
e

B
d

C
f

D
a

E
None of the above

Solution

'c' is opposite 'a'.
Hence, when 'c' is at the top, 'a' will be at the bottom.
Question 9
1 / -0

Directions: Study the three different orientations of a cube given below and answer the question that follows.

Which of the following numbers appears on the face opposite to the one having 2?

A
1

B
4

C
5

D
3

Solution

If two faces of two orientations of a same die are same, then the remaining faces are opposite each other.
In figure (1) and figure (2), we get that 3 and 6 are adjacent to each other (with same orientation) and therefore, 5 must be opposite 2.
Question 10
1 / -0

Directions: Study the three different orientations of a cube given below and answer the question.

The number on the face opposite to the one having 6 is

A
1

B
4

C
5

D
2

Solution

From orientations 1 and 3, it can be observed that 4 appears on the face opposite to the one with 6.