A cube of side 10 cm is painted on all its side. If it is sliced into 1 cc cubes, how many 1 cc cubes will have exactly one of their sides painted?a)146b)378c)486d)None of theseCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

To solve this problem, we need to visualize the cube and the small 1 cc cubes that are formed when it is sliced.

- A cube has 6 faces, so when all sides of the cube are painted, all 6 faces are painted.
- Each face of the cube is a square with side length 10 cm, which means it is made up of 100 smaller squares with side length 1 cm.
- When the large cube is sliced into 1 cc cubes, each small cube will have one of its sides painted if and only if it is located on the edge of the large cube.

Now let's calculate the number of small cubes that are located on the edges of the large cube.

- The large cube has 12 edges, and each edge has a length of 10 cm.
- Each edge is made up of 10 smaller cubes, as there are 10 cubes along the length of the edge.
- So, there are a total of 12 edges * 10 cubes per edge = 120 small cubes on the edges of the large cube.

However, we need to remember that the corners of the large cube are counted twice in the above calculation.

- The large cube has 8 corners, and each corner is made up of 3 edges.
- Each corner is formed by the intersection of 3 edges, so it is counted 3 times in the above calculation.
- So, there are a total of 8 corners * 3 times per corner = 24 small cubes at the corners of the large cube.

Therefore, the total number of small cubes that have exactly one of their sides painted is:

- Number of cubes on the edges: 120 cubes
- Number of cubes at the corners: 24 cubes
- Total = 120 cubes + 24 cubes = 144 cubes

Since the options provided do not include the correct answer, we can conclude that the correct answer is None of these (option D).

Similar SSC Doubts

Little wooden cubes, each with a side of one inch, are put together to form a solid cube with a side of three inches. This big cube is then painted red all over on the outside. When the big cube is broken up into the original little ones, how many cubes will have paint on two sides?

Little wooden cubes, each with a side of one inch, are put together to form a solid cube with a side of three inches. This big cube is then painted red all over on the outside. When the big cube is broken up into the original little ones, how many cubes will have paint on two sides?

Little wooden cubes each with a side of one inch are put together to form a solid cube with a side of three inches. This big cube is then painted red all over on the outside. When the big cube is broken up into the original little ones, how many cubes will have paint on two sides?

A cube, painted with a certain colour (Re d) on the outer surface, is of 2 inches height, 2 inches wide and 2 inches across. If it’s cut into one-inch cubes as shown by dotted lines, indicate the number of cubes having colour (Red) at least on two sides?

Study the following information carefully and answer the given questions :A, B, C, D, E, F, G and H are sitting around a square table facing the centre in such a way that four of them sit at four corners of the square while four sit in the middle of each of the flour sides.(

Top Courses for SSC

Suggested Free Tests

Related Content

Mock Test Series

Related Question Answers

Other Engg Branches

Related Exams

Company