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The roof of a certain bell tower is in the shape of a square pyramid
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12 Sep 2021, 04:43
12 Sep 2021, 04:43
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The roof of a certain bell tower is in the shape of a square pyramid with a length and width of 20ft and a lateral height of 18ft. The roof needs new tiles, which are 72 square inches in size. The tiles must overlap so that water does not leak between the seams. What is the minimum number of tiles needed to cover the roof (minimum wastage), assuming 20% extra to account for the overlap?
A. 432
B. 518
C. 1440
D. 1728
E. None of the above
Qs edited on 23-Sep 2021
A. 432
B. 518
C. 1440
D. 1728
E. None of the above
Qs edited on 23-Sep 2021
Re: The roof of a certain bell tower is in the shape of a square pyramid
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12 Sep 2021, 22:55
12 Sep 2021, 22:55
Please Explain with figure if possible .
Re: The roof of a certain bell tower is in the shape of a square pyramid
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23 Sep 2021, 07:05
23 Sep 2021, 07:05
1
Since it is a square pyramid, we need to cover 4 triangle-shaped faces. The problem gives us the length of the base (20) and the height (18) for each of these triangles. Since 1ft = 12 inches, we have the area of each triangle is (1/2)*(18*12)*(20*12) = 25,920 square inches.
Assuming 20% extra surface for overlap, and multiplying by 4 to cover all 4 faces, we have the total surface to be covered is 1.2*4*25,920 = 124,416.
Finally, using the fact that each tile measures 72 square inches, we divide and get 124,416/72 = 1,728.
However, the OA is 1,440, which is identical to everything I did here but for taking the 20% extra surface that the problem says is needed.
I appreciate it if someone can point out where I am making a mistake.
Assuming 20% extra surface for overlap, and multiplying by 4 to cover all 4 faces, we have the total surface to be covered is 1.2*4*25,920 = 124,416.
Finally, using the fact that each tile measures 72 square inches, we divide and get 124,416/72 = 1,728.
However, the OA is 1,440, which is identical to everything I did here but for taking the 20% extra surface that the problem says is needed.
I appreciate it if someone can point out where I am making a mistake.
