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)
To find the total amount of nylon needed to make 50 tea bags, we first need to calculate the surface area of one triangular pyramid tea bag.
The surface area of a triangular pyramid can be calculated using the formula:
Surface Area = Base Area + 1/2 * Perimeter of Base * Slant Height
First, let's calculate the base area of the equilateral triangle:
Base Area = (1/2) * base * height
Base Area = (1/2) * 40 mm * 35 mm
Base Area = 700 mm^2
Next, let's calculate the perimeter of the base of the equilateral triangle:
Perimeter = 3 * base
Perimeter = 3 * 40 mm
Perimeter = 120 mm
Now, let's calculate the total surface area of one tea bag:
Surface Area = 700 mm^2 + 1/2 * 120 mm * 45 mm
Surface Area = 700 mm^2 + 5400 mm^2
Surface Area = 6100 mm^2
Finally, let's calculate the total amount of nylon needed to make 50 tea bags:
Total Area = 6100 mm^2 * 50 tea bags
Total Area = 305,000 mm^2
Therefore, 305,000 mm^2 of nylon is needed to make 50 tea bags.
The answer choices are 3400 170,000, 150,000 or 3000
Apologies for the mistake in my previous response. Let's correct the calculation.
Given:
Base Area = 700 mm^2
Perimeter = 120 mm
Slant Height = 45 mm
Surface Area for one tea bag:
Surface Area = Base Area + 1/2 * Perimeter * Slant Height
Surface Area = 700 + 1/2 * 120 * 45
Surface Area = 700 + 2700
Surface Area = 3400 mm^2
Total Surface Area needed for 50 tea bags:
Total Area = 3400 mm^2 * 50 tea bags
Total Area = 170,000 mm^2
Therefore, the correct answer choice is 170,000.