To calculate the total surface area of one nylon tea bag in the shape of a triangular pyramid, we first need to calculate the area of the equilateral triangle, then find the area of the three triangular faces, and finally add the base area.
1. Area of equilateral triangle:
Area = (sqrt(3)/4) * side^2
Area = (sqrt(3)/4) * 40^2
Area = 693.37 mm^2
2. Area of each triangular face:
Area = (1/2) * base * slant height
Area = (1/2) * 40 * 45
Area = 900 mm^2
3. Total surface area of one nylon tea bag:
Total area = 3 * 900 + 693.37
Total area = 3393.37 mm^2
4. Total nylon needed for 50 tea bags:
Total nylon = 3393.37 * 50
Total nylon = 169,668.5 mm^2
Therefore, the amount of nylon needed to make 50 tea bags is 169,668.5 mm^2, which is closest to 170,000 mm^2.
A factory makes nylon tea bags. The bags are in the shape of a triangular pyramid. How much nylon is needed to make 50 tea bags given the following dimensions?
Base of the equilateral triangles: 40 mm
Height of the base triangle: 35 mm
Slant height of the equilateral triangular faces: 45 mm
(1 point)
Responses
153,125 mm2
153,125 mm squared
170,000 mm2
170,000 mm squared
3,400 mm2
3,400 mm squared
3,062.5 mm2
3,062.5 mm squared
1 answer