**Category : **9th Class

**Type-I (Number of cubes/blocks in a solid)**

In such type of problems, a solid made up of many identical cubes or blocks/cuboids is given. A student is required to count all these cubes or blocks/cuboids.

**EXAMPLE**

**1. Count the number of cubes in the given figure. **

(a) 8 (b) 9 (c) 12 (d) 15

**Explanation (d):**

There are 4, 4 and 1 columns each containing 1, 2 and 3 cubes respectively.

So number all possible cubes \[=\left( 4\times 1 \right)+\left( 4\times 2 \right)+\left( 1\times 3 \right)=15.\]

**Type-II (Construction of boxes)**

In such type of problems a net of a cube or cuboid is given and a student is asked to identify the cube or cuboid formed from this net.

**2. A sheet of paper is given in Fig. (X) which has to be folded to form a box.**

Choose a box from amongst the alternatives, that is similar to the boxes formed.

(a) S only (b) Q and S only (c) P and R only (d) R only

**Explanation (b):**

The opposite faces of the box so formed are: A and E, B and D, C and F.

The option (b) fulfills this condition.

**Type-III (Problems on Dice faces)**

In such type of problems the same dice is shown in various positions.

A student is required to observe these positions and then answer the given question.

**3. The four different positions of a dice are given below.**

**How many dots are there on the face opposite the face with three dots?**

(a) 2 (b) 4 (c) 5 (d) 6

**Explanation (c):**

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.

*play_arrow*Cubes and Dice

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