The roof of a building is shaped like a square pyramid, with a base of 18m by 18m. If the slant height of the roof is 12m and roofing costs 5.75m2, how much will it cost for roofing material?
This is the last question for my homework could u answer this for me to find how much the cost is?
Thanks.
To find the cost of roofing material, we first need to calculate the total surface area of the roof.
The surface area of a square pyramid is given by the formula:
Surface Area = base area + (0.5 × perimeter of base × slant height)
Let's calculate the base area:
Base area = length × width
= 18m × 18m
= 324m²
Now, let's calculate the perimeter of the base:
Perimeter of base = 4 × length
= 4 × 18m
= 72m
Finally, let's calculate the surface area of the roof using the formula above:
Surface Area = 324m² + (0.5 × 72m × 12m)
= 324m² + (36m × 12m)
= 324m² + 432m²
= 756m²
The surface area of the roof is 756m².
Now, let's calculate the cost of roofing material:
Cost = Surface Area × Cost per square meter
= 756m² × $5.75/m²
= $4,347
Therefore, it will cost $4,347 for the roofing material.