Cubes Test

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Cubes Test - 1

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Question 1
1 / -0

Directions For Questions

Read the following information and answer the given question.

A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes obtained are now separated.

...view full instructions

How many smaller cubes have no coloured face?

A
24

B
16

C
8

D
10

Solution

Number of smaller cubes with no face coloured = (n – 2)³ = (4 – 2)³ = 8
Question 2
1 / -0

Directions For Questions

Read the following information and answer the given question.

A cube is painted red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes obtained are now separated.

...view full instructions

How many smaller cubes will have at least two faces painted red?

A
4

B
8

C
32

D
24

Solution

Concept: If a cube is cut in to n³ smaller cubes then-
Number of cubes with 0 side painted= (n - 2)³
Number of cubes with 1 side painted =6(n - 2)²
Number of cubes with 2 sides painted= 12(n - 2)
Number of cubes with 3 sides painted= 8(always)

In the given question a red color painted cube is cut into 4³ smaller cubes.
So, here n = 4.

Number of smaller cubes with at least two faces painted red = Number of cubes with three faces painted red + Number of cubes with two faces painted red
Number of cubes with three faces painted red = 8 (all corners of the cubes)
Number of cubes with two faces painted red = 12(n - 2) = 12 x 2 = 24
Number of smaller cubes with at least two faces painted red = 24 + 8 = 32
Question 3
1 / -0

Directions For Questions

Read the following information and answer the given question.

A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes so obtained are now separated.

...view full instructions

How many smaller cubes have only two surfaces painted with red colour?

A
24

B
8

C
12

D
20

Solution

Number of smaller cubes with two surfaces painted red = (n – 2) × 12 = (4 – 2) × 12 = 24
Question 4
1 / -0

Directions For Questions

Read the following information and answer the given question.

A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes so obtained are now separated.

...view full instructions

How many smaller cubes have only three surfaces painted with red colour?

A
0

B
12

C
24

D
8

Solution

Number of smaller cubes with three surfaces painted red = 8
All the small cubes on the vertices of large cube have three faces coloured.
Question 5
1 / -0

Directions For Questions

Read the following information and answer the question given below.

A cube is painted red on two adjacent faces, black on the faces opposite to the red faces, and green on the remaining faces. Now, the cube is cut into 64 smaller cubes of equal size.

...view full instructions

How many smaller cubes will have no painted face?

A
0

B
4

C
8

D
16

Solution

Number of smaller cubes with no painted face = (4 - 2)³ = (2)³ = 8.

The 8 cubes at the core will have no painted face.