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.
1. Count the number of cubes in the given figure.
(a) 8 (b) 9 (c) 12 (d) 15
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
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
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.
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