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15 Sep 2021, 05:15
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C
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37% (02:39) correct
63%
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based on 46
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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 (no wastage), assuming 20% extra to account for the overlap?
A. 432
B. 518
C. 1440
D. 1728
E. None of the above
A. 432
B. 518
C. 1440
D. 1728
E. None of the above
15 Sep 2021, 05:33
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IMO Option D
Since length and breadth are equal hence all for sides can be considered equal triangles with base as 20ft and height as 18ft
Area of 1 side of the pyramid roof = 0.5 x 20 x 18 x 144 inches [changing ft to inches]
Area of 4 sides of the pyramid roof = 2 x 20 x 18 x 144 inches (considering 4 sides)
Number of tiles required (with 20% extra to account for the overlap)
2 x 20 x 18 x 144 * 1.2 / 72 = 1728 tiles
Since length and breadth are equal hence all for sides can be considered equal triangles with base as 20ft and height as 18ft
Area of 1 side of the pyramid roof = 0.5 x 20 x 18 x 144 inches [changing ft to inches]
Area of 4 sides of the pyramid roof = 2 x 20 x 18 x 144 inches (considering 4 sides)
Number of tiles required (with 20% extra to account for the overlap)
2 x 20 x 18 x 144 * 1.2 / 72 = 1728 tiles
12 Jan 2022, 00:31
Kudos
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The roof is in the shape of a square pyramid with a length and width of 20ft and a lateral height of 18ft. Now, to cover the roof with tiles we have to only consider the area of 4 isosceles triangles with base 20 ft and slant height 18 ft. (Kindly refer to the image below)
The HEIGHT of each triangle = √18^2-10^2 = √224 ≈ 15 ft
Area of each triangle = 1/2*Base*Height = 1/2*20*15 = 150 ft^2
Total area to be covered = 4*150 = 600 ft^2
Area of tile in square foot = 72/144 = 0.5 ft^2
No. of tiles required to cover the area mentioned above = 600/0.5 = 1200 tiles
Minimum number of tiles needed to cover the roof (no wastage), assuming 20% extra to account for the overlap = 1.2*1200 = 1440 tiles (C)
The HEIGHT of each triangle = √18^2-10^2 = √224 ≈ 15 ft
Area of each triangle = 1/2*Base*Height = 1/2*20*15 = 150 ft^2
Total area to be covered = 4*150 = 600 ft^2
Area of tile in square foot = 72/144 = 0.5 ft^2
No. of tiles required to cover the area mentioned above = 600/0.5 = 1200 tiles
Minimum number of tiles needed to cover the roof (no wastage), assuming 20% extra to account for the overlap = 1.2*1200 = 1440 tiles (C)
Attachments
Square-Pyramid-2.jpg [ 36.71 KiB | Viewed 1795 times ]
