Cubes Test

Result

Cubes Test - 2

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Question 1
1 / -0

Directions For Questions

A cube is painted red on two adjacent surfaces, black on the surface opposite to red surfaces 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 have less than three surfaces painted?

A
8

B
24

C
28

D
56

Solution

Number of smaller cubes with less than three surfaces painted = Number of cubes with two surfaces painted + Number of cubes with one surface painted + Number of cubes with no surface painted = 12(n - 2) + 6(n - 2)² + (n - 2)³ = 12(4 - 2) + 6(4 - 2) ² + (4 - 2)³ = 24 + 24 + 8 = 56
Question 2
1 / -0

Directions For Questions

Read the following information and answer the given question.

A cube is painted red on two adjacent surfaces, black on the surface opposite to the red surfaces 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 have three surfaces painted?

A
4

B
8

C
16

D
24

Solution

Number of smaller cubes with three surfaces painted = 8
Question 3
1 / -0

Directions For Questions

Read the following information and answer the given question.

A cube is painted red on two adjacent surfaces, black on the surface opposite to the red surfaces 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 with two surfaces painted have one face green and one of the adjacent faces black or red?

A
8

B
16

C
24

D
28

Solution

Green painted surfaces are on the upper and lower surfaces of the cube. Hence, two surfaces painted with one surface green and another black or red will be present at the edges on the upper and bottom surfaces. Their number is (n – 2) × 8 = 16.
Question 4
1 / -0

A cube is painted red on two adjacent surfaces and black on the surface opposite to red surfaces and green on the remaining faces. Now, the cube is cut into 64 smaller cubes of equal size. How many smaller cubes have at least one surface painted green?

A
8

B
24

C
32

D
56

Solution

All the smaller cubes present on the top and bottom of the big cube have green colour on at least one of its surfaces.
Required answer = 16 + 16 = 32
Question 5
1 / -0

Directions For Questions

A cube is coloured red on two opposite faces, blue on two adjacent faces and yellow on two remaining faces. It is then cut into two halves along the plane parallel to the red faces. One piece is then cut into four equal cubes and the other one into 32 equal cubes.

...view full instructions

How many cubes do not have any coloured face?

A
0

B
16

C
4

D
8

Solution

Only four smaller cubes from inside the cube will have none of their faces painted.