"Published in Newark, California, USA"
A football stand 150 yd. long has 20 tiers of seats; each tier has a rise of 2 ft. and tread of 3 ft. It is constructed of reinforced concrete with a cross section as shown. Find the amount of material used in its construction.
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
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| Photo by Math Principles in Everyday Life |
The first thing that we need to do is to isolate the given figure which is the 20 tiers of seat section as follows
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| Photo by Math Principles in Everyday Life |
At the first layer, there is one block whose dimension is 2' x 3'. At the second layer, there are two blocks. At the third layer, there are three blocks, and so on. We need to get the total number of blocks so that we can get the area of the section. Since there's a sequence of number of blocks for each layer by arithmetic progression, then we can get the total number of blocks by using the sum of n terms as follows
The total area of blocks is
The area of a triangle is
Hence, the area of the 20 tiers of seat section which is the base of a prism is
Therefore, the amount of material used for the construction of a football stand which is a prism is
