Dice Test

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Dice Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

Directions For Questions

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.

...view full instructions

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 2
1 / -0

Directions For Questions

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.

...view full instructions

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 3
1 / -0

Directions For Questions

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.

...view full instructions

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 4
1 / -0

Directions For Questions

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.

...view full instructions

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