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A cube painted blue on all faces is cut into 27 small cubes of equal size. How many small cubes are painted on one face only?
The big cube can be cut into 27 small cubes as shown in the figure.
Number of cubes only one face painted = (m − 2)^{2} × 6
= (3 − 2)_{2} × 6 = (1)^{2} × 6 = 6.
A cube is painted red on all faces is cut into 27 small cubes of equal size then how many cubes are not painted on any face?
There is only one cube which is not painted on any face.
A cube of side 10cm is coloured green with a 2 cm wide red strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size then how many cubes are without any colour?
There are 9 central cubes in three middle layers, which are without any colour.
∴ No. of cubes without any colour = 9 × 3 = 27
How many dots are there on the dice face opposite the one with three dots?
From figures (i), (ii), (iv) we observe that 6, 4, 3, 1 lie adjacent to 2. Hence the number 5 will appear on the face showing 2.
Three positions of a dice are given. Based on them find out which number is found opposite the number 2 in the given cube.
From figures (i) & (ii), it is clear that 1, 4, 3, 5 lie adjacent to number 6. So, number 2 lies opposite to 6.
In the given figure find the number of dots on the face opposite the face having 3 dots.
From figures (i), (ii) and (iii), we conclude that 3, 4, 6 and 1 dots appear adjacent to 2 dots. Therefore, 5 dots appear opposite 2 dots. Now, from figures (i) and (iii), we conclude that 2, 4 and 1 dots appear adjacent to 3 dots. Therefore, either 5 or 6 dots appear opposite 3 dots. Since, 5 dots appear opposite 2 dots, it follows that 6 dots appear opposite 3 dots.
Two positions of a dice are shown. When 4 is at the bottom, what number will be on the top?
From figure (i) & (ii) 2, 3, 5, 6 lie adjacent to 1. 4 lies opposite to 1.
In the given figure, when 4 is at the bottom, what number will be on the top?
When 4 is at the bottom then 3 will be on the top.
Two positions of a parallelepiped are given below. When the number 3 will be on the top side then which number will be at the bottom?
If 3 will be on the top, then 5 will come at bottom.
Three different positions X, Y, Z of a dice are as shown below.
Which number lies opposite to 6?
From positions X and Y we conclude that 1, 5, 6 and 3 lie adjacent to 4. Therefore, 2 must lie opposite 4. From positions Y and Z we conclude that 4, 3, 2 and 5 lie adjacent to 6. Therefore, 1 must lie opposite 6.
In the given figure, which number lies at the bottom face in position B?
From positions A and B we conclude that 1, 5, 6 and 3 lie adjacent to 4. Therefore, 2 must lie opposite 4. From positions A and B we conclude that 4, 3, 2 and 5 lie adjacent to 6. Therefore, 1 must lie opposite 6. Thus, 2 lies opposite 4, 1 lies opposite 6 and consequently 5 lies opposite 3.
2 lies at the bottom face in position B.
In the following figure, which symbol is opposite to the arrow.
(B) 'From Figs (i) and (ii) it is clear that triangle appears opposite arrow'.
Two positions of a block are given below. When 1 is at the top, which number will be at the bottom?
2 is common to the two positions of the dice. If the dice in figure (i) is rotated so that 2 remains on the top face and the numbers 3 & 6 move to the face hidden behind 5 & 1 respectively. 5 lies opposite to 3 and 6 lies opposite to 1.
In the given figure, when 2 is at the bottom, what number will be at the top?
When 2 is at the bottom 1 will be at the top.
Cubes of same size are arranged in the form of cube on a table then a column of five cubes is removed from each of the four cubes is removed from each of the four corners. All the exposed faces of rest of the cube are coloured yellow. Then how many small cubes are there in the solid after the removal of the column?
Required no. of cubes = 125 – (4 × 5)
= 125 – 20 = 105
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