To find the surface area of one triangular pyramid tea bag, we first need to find the area of the equilateral triangle base:
Area of equilateral triangle = (sqrt(3) / 4) * (side)^2
Area = (sqrt(3) / 4) * 40^2
Area = (sqrt(3) / 4) * 1600
Area = 347.70 sq. units
Next, we need to find the area of the 3 triangular faces:
Area of triangular face = (1/2) * base * height
Area = (1/2) * 40 * 35 = 700 sq. units
Now, we can calculate the total surface area of one tea bag:
Total surface area = (3 * area of triangular face) + area of base
Total surface area = (3 * 700) + 347.70
Total surface area = 2100 + 347.70
Total surface area = 2447.70 sq. units
Since we are making 50 tea bags, the total nylon needed for all 50 tea bags would be:
Total nylon needed = 2447.70 sq. units * 50
Total nylon needed = 122,385 sq. units
Therefore, 122,385 sq. units of nylon is needed to make 50 tea bags.
A factory makes nylon tea bags. The bags are the shape of a triangular pyramid. How much nylon is needed to make 50 tea bags?
Base of equilateral triangles 40
Height of base triangle 35
Slant height of equilateral triangular faces 45
1 answer
1 answer