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
170,000 mm2
170,000 mm squared
3,062.5 mm2
3,062.5 mm squared
3,400 mm2
3,400 mm squared
153,125 mm2
wrong
To calculate the total amount of nylon needed to make 50 tea bags, we first need to calculate the total surface area of one tea bag.
1. Calculate the area of the equilateral triangle:
Area = (base * height) / 2
Area = (40 mm * 35 mm) / 2
Area = 1400 mm2
2. Calculate the area of one triangular face (using slant height):
Area = (base * slant height) / 2
Area = (40 mm * 45 mm) / 2
Area = 900 mm2
3. Calculate the total surface area of one tea bag (including the base):
Total Area = 2 * (1400 mm2) + 3 * (900 mm2)
Total Area = 2800 mm2 + 2700 mm2
Total Area = 5500 mm2
4. Calculate the total amount of nylon needed for 50 tea bags:
Total Nylon = 50 tea bags * 5500 mm2
Total Nylon = 275,000 mm2
Therefore, the correct answer is:
275,000 mm2
Apologies for the mistake in the previous calculation. Let's correct this:
1. Calculate the area of the equilateral triangle (base * height / 2):
Area = (40 mm * 35 mm) / 2
Area = 1400 mm²
2. Calculate the total surface area of one triangular face (base * slant height / 2):
Area = (40 mm * 45 mm) / 2
Area = 900 mm²
3. Calculate the total surface area of one tea bag (including the base):
Total Area = 2 * 1400 mm² + 3 * 900 mm²
Total Area = 2800 mm² + 2700 mm²
Total Area = 5500 mm²
4. Calculate the total amount of nylon needed for 50 tea bags:
Total Nylon = 50 tea bags * 5500 mm²
Total Nylon = 275,000 mm²
Therefore, the correct answer is:
275,000 mm²