Find the number of cubes in the given figures
To find the number of cubes in the given figure, we need to carefully count each visible cube and ensure we account for any cubes that might be hidden behind others.
Thus, the total number of cubes in the structure is 15.
Correct Option: D) 15
A cube of side 12 cm is painted green on all the faces and then cut into smaller cubes of sides 2 cm each. Find the number of smaller cubes that have only one face painted.
To find the number of smaller cubes with only one face painted, we need to determine the number of smaller cubes along each edge of the larger cube. Then, we can use the formula for cubes with one face painted, which are located on the faces of the larger cube but not on the edges or corners.
D) 96
Two positions of the same dice are given, which of the following number will be opposite to 5?
To determine which number is opposite to 5 on the dice, we need to analyze the two given positions of the dice and identify the numbers that are adjacent to 5 in both positions.
Correct Option: A) 2
A dice is numbered from 1 to 6 in different ways. If 2 is opposite to 3 and adjacent to 4 and 6, then which of the following statements is necessarily true?
1 is opposite to 5
4 is opposite to 6
4 is adjacent to 2 and 6
1 is adjacent to 2 and 3
We need to determine the arrangement of numbers on a dice based on the given conditions. A standard dice has 6 faces, and opposite faces never share an edge. We will use the given information to deduce the positions of the numbers and then evaluate each statement.
If 2 is opposite 3, and 2 is adjacent to 4 and 6, then the remaining two faces adjacent to 2 must be 1 and 5. This means 1 and 5 are also adjacent to 2.
Consider the faces 4 and 6. They are adjacent to 2. Since 2 is opposite 3, 4 and 6 cannot be opposite 3. Also, 4 and 6 cannot be opposite 2 (as they are adjacent to 2).
The pairs of opposite faces on a dice are (2, 3), and two other pairs from the remaining numbers {1, 4, 5, 6}.
Since 4 and 6 are adjacent to 2, they cannot be opposite to 2. Also, 4 and 6 cannot be opposite to 3 (because if 4 was opposite 3, then 4 would be adjacent to 2, which is true, but then 4 would not be adjacent to 3, which is also true. However, this doesn't help much yet).
Let's list the numbers: {1, 2, 3, 4, 5, 6}.
We know 2 is adjacent to 4 and 6. This means 4 and 6 are not opposite to 2. Also, 4 and 6 cannot be opposite to 3 (because if 4 was opposite 3, then 4 would be adjacent to 2, which is given. But if 4 is opposite 3, then 4 cannot be adjacent to 3, which is always true for opposite faces).
The key is that 4 and 6 are adjacent to 2. This implies 4 and 6 are NOT opposite to 2. The faces adjacent to 2 are 1, 4, 5, 6. The faces adjacent to 3 are 1, 4, 5, 6.
Consider the faces 4 and 6. They are adjacent to 2. Can 4 be opposite to 6? If 4 is opposite to 6, then the remaining pair (1, 5) must be opposite each other. In this case, 2 would be adjacent to 1, 3, 4, 5. But we are given 2 is adjacent to 4 and 6. This means 4 and 6 are not opposite.
Therefore, 4 and 6 must be adjacent to each other. This means the remaining two numbers, 1 and 5, must be opposite each other. So, the opposite pairs are (2, 3), (1, 5), and (4, 6).
Opposite pairs: (2, 3), (1, 5), (4, 6).
Adjacent to 2: 1, 4, 5, 6. (Since 2 is opposite 3, all other numbers are adjacent to 2).
The problem states 2 is adjacent to 4 and 6. This is consistent with our deduction.
D) 1 is adjacent to 2 and 3
A cube has six different symbols drawn over its six faces. The symbols are dot, circle, triangle, square, cross and arrow. Three different positions of the cube are shown in figures X, Y, and Z. Which symbol is opposite the Square?
To determine which symbol is opposite the square on the cube, we need to analyze the positions of the symbols on the visible faces of the cube in the given diagrams.
Correct Option: D) Circle
Find the number of cubes in the given figure
To find the number of cubes in the given figure, we need to carefully count each visible cube and ensure that no cubes are double-counted.
Correct Option: C) 10
