# Cubes and Dice Questions

A) 130 | B) 132 |

C) 138 | D) 140 |

Explanation:

In the figure, there are

5 columns containing 4 cubes each;

33 columns containing 3 cubes each;

9 columns containing 2 cubes each and 3 columns containing 1 cube each.

$\therefore $ Total Number of cubes = ( 5 x 4) + (33 x 3) + (9 x 2) + (3 x 1) = 20 + 99 + 18 + 3 = 140

A) 2 | B) 4 |

C) 5 | D) 6 |

Explanation:

From figures (i), (ii) and (iv), we conclude that 6, 4,1 and 2 dots appear adjacent to 3 dots. Clearly, there will be 5 dots on the face opposite the face with 3 dots.

A) 2 is opposite to 6 | B) 1 is adjacent to 3 |

C) 3 is adjacent to 5 | D) 3 is opposite to 5 |

Explanation:

If 1 is adjacent to 2, 4 and 6 then either 3 or 5 lies opposite to 1. So, the numbers 3 and 5 cannot lie opposite to each other. Hence, 3 is adjacent to 5 (necessarily).

A) 4 is adjacent to 6 | B) 2 is adjacent to 5 |

C) 1 is adjacent to 6 | D) 1 is adjacent to 4 |

Explanation:

If 1 is adjacent to 2, 3 and 5, then either 4 or 6 lies opposite to 1. So, the numbers 4 and 6 cannot lie opposite to each other. Hence, 4 necessarily lies adjacent to 6.

A) Option 1,2 and 3 | B) Option 1,3 and 4 |

C) Option 2 and 3 | D) Option 2,3 and 4 |

Explanation:

When the sheet in fig. (A) is folded, then one of the faces of the cube formed will be of the form and this face will lie opposite the face bearing a square. Also, one of the blank faces lies opposite another blank face and the third blank face lies opposite the face bearing an '=' sign. Clearly, all the three blank faces cannot appear adjacent to each other. So, the cube shown in fig. (2) which has all the three blank faces adjacent to each other cannot be formed. Hence, only the cubes shown in figures A, C and D can be formed.

A) 56 | B) 48 |

C) 32 | D) 64 |

Explanation:

We know that Cubes with no surface painted can be find using ${\left(x-2\right)}^{3}$, where x is number of cuttings. Here x=6.

$\therefore {\left(6-2\right)}^{3}=64$

A) 12 | B) 13 |

C) 15 | D) Cannot be determined |

Explanation:

In a usual dice, the sum of the numbers on any two opposite faces is always 7. Thus, 1 is opposite 6, 2 is opposite 5 and 3 is opposite 4.

Consequently, when 4, 3, 1 and 5 are the numbers on the top faces, then 3, 4, 6 and 2 respectively are the numbers on the face touching the ground. The total of these numbers = 3 + 4 + 6 + 2 = 15.

A) 2 | B) 3 |

C) 6 | D) Cannot be determined |

Explanation:

We shall assume the dice in fig. (ii) to be rotated so that the 5 dots appear at the same position as in fig. (i) i.e. on RHS face (i.e. on face II as per activity 1) and 1 dot appears at the same position as in fig; (i) i.e. on Front face (i.e. on face I). Then, from the, two figures, 2 dots appear on the top face (i.e. on face V) and 4 dots appear on the Bottom face (i.e. on face VI).

Since, these two faces are opposite to each other, therefore, two dots are contained on the face opposite to that containing four dots.