I'm receiving frequent requests for solving the question on "counting the number of faces" that appeared in CEED 2013 question paper (as shown below). This is a complex geometric solid, which will probably confuse you and will consume more time.
For this, I had given step-by-step solution in the form of pictures with arrows to locate the faces. Remember that you need to visualize this mentally, for arriving to the final answer without putting pen or pencil on paper to save time.
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Here is my latest post - Improve imagination, work with 3D solids and unfolding of solid shapes
Now, as discussed in my other posts (Working with geometric objects), we will count the number of faces following the order :
Front > Right > Back > Left > Top > Bottom
Let us now count the faces from front direction. As you can see I considered the semi-circular portion (numbered 5) as a single surface. So totally you will be counting 6 faces.
Now count the number of faces from the right direction as shown below. Note that I counted the two slant surfaces ( numbered 5 and 6) in this direction. You may even count the slant surfaces from front direction, provided you neglect the same from right side view. It's up to you to decide and count.
Counting for number of faces from back side will give four faces as shown in the below picture.
Counting from Left direction is a bit trickier, as you may visualize only one surface, but in fact you should be seeing two surfaces as shown in the picture below. Remember that the surfaces which are not in the same plane cannot be counted as a single face.
Now, we will count the number of faces that can be seen from top direction. You should be counting four faces as shown below.
Finally, you need to count the number of faces from bottom. I visualize only one surface, because all the individual shapes are in same plane. Thus summing up the counting in all directions, you should now get 23 as answer (option 2). I hope you enjoyed doing this.
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Here's my video guide on how to easily solve number of faces problem and what mistakes to avoid