21-07-2021 Answer

 216 cubes of similar size are arranged in the form of a bigger cube. The six faces of the bigger cube are painted with green, red, blue, violet, white, pink colours.

Related Comprehension Questions

1. How many cubes are painted with red or blue?

Answer: 66 or 72

Solution: In one face 36 smaller cubes will be present. When red and blue are not adjacent 36*2=72 cubes will be painted with red or blue. When these colours are in adjacent faces, the six common cubes are to be subtracted giving 72-6=66

2. How many cubes are painted with red or blue or green?

Answer: 91 or 96

Solution: When all three colours are adjacent to each other, we get 36 + 30 + 25 = 91 (We subtract the common cubes from 36 and hence 30 and 25)

When one of the three colours is in between the other two, we get 36+30+30 = 96

3. How many cubes are painted with red or blue but not green?

Answer: 55 or 60

Solution: When all three colours are adjacent to each other, we get 30+25 = 55

When green coloured face is in between the other two, we get 30+30 = 60

When green coloured face is just adjacent to one of the colours, we get 36+24 = 60

4. How many cubes are painted with red, blue, green and violet?

Answer: NOT

Solution: Because none of the cubes can be painted with four colours.

5. Smita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of cubes needed to make a hollow cube looking of the same shape?

Answer: 98

Solution: The formula =lwh -  (l-2a)(w-2a)(h-2a); Here l=w=h=5 and a=1.

So the number of cubes required for making a hollow cube =(5*5*5)-((5-2*1)(5-2*1)(5-2*1)) = 98 cubes

6. The below diagram depicts various views of a cube. Find the number or letter present in the face opposite to 3.

Diagram: 

Answer: Z

Solution: Numbers or letters on opposite faces are (2,Y) (3,Z) (1,Y)

7. Six faces of a cube are painted with different colors. Two different views of the cube are shown in the image below. Which color is present in the face of the cube opposite to Brown?

Diagram: 

Answer: Blue

Solution: the first view should be rotated 90 degree in anti clock wise direction and tilted so that Yellow is at the bottom; Thus Violet is opposite to Yellow and Brown and Blue are in opposite to each other

8. A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

Answer: 488

Solution: Side of cube = 5 cm and its thickness = 1 cm

so volume of outer cube = 5*5*5  volume of inner cube = 3*3*3 (as 1cm is taken off at both ends)

volume of the hollow cube = 5*5*5 - 3*3*3 = 125-27 = 98

So total no of small cubes of the size 1 cm = 98/1*1*1 = 98

We know a cube has 6 faces so total no of face = 98*6 = 588

One surface of outer cube contains a total of 25 surface of smaller cube , so when 4 surfaces of outer cube is painted total no of surface of small cubes i.e supposed to be painted is 4*25 = 100

So the total no of surfaces of small cube that will be remained unpainted is 588-100 = 488

9. All faces of a cube with 8m edge is painted red. If a cube is cut into a smaller cube with a 2m edge, how many of the 2m cubes have been painted exactly on one face?

Answer: 24

Solution: The cubes on the edges will be painted on more than one face.

Hence number of cubes = 6 * 4 = 24 (A cube has 6 sides and in each side 4 cubes are there with just one side painted)

10.The below diagram depicts various views of a cube.

Diagram: 

Find the letter that replaces the question mark.

Answer: Q

Solution: Letters on opposite sides are (N,M) (P,Q) (L,O)

11. The below diagram depicts various views of a cube.

Diagram: 

Find the number present in the face opposite to 1 in the cube.

Answer: 3

Solution: Comparing the adjacent sides 3 comes the answer

12. The below diagram depicts various views of a cube.

Diagram: 

Find the letter that replaces the question mark.

Answer: T

Solution: T and S are on opposite sides, P and U are on opposite sides, R and Q are on opposite sides

13. How many points will be on the face opposite to in face which contains 2 points?

Answer: 6

Solution: From 1st image and 3rd in the series, 1 point, 3 points and 5 points will not be on the opposite side.

So possible points are 4 and 6; From 2nd and 4th image in the series, 4 points side has 1 point and 5 adjacent to it.

Hence from above two, 1,3,5 and 4 are adjacent. Hence 4 cannot be opposite to 2 points.

14. The below diagram depicts various views of a cube. Find the number or letter present in the face opposite to 6 .

Diagram: 

Answer: O

Solution: Opposite faces contain (6,O) (5,M) (4,N)

15. The below diagram depicts various views of a cube.

Diagram: 

Find the number or the letter that replaces the question mark.

Answer: B

Solution: Opposite face pairs are (A,B) (1,2) (3,C)