How much nylon is needed to make 50 tea bags in shape of triangular pyramid . Dimensions 40mm 35mm 45mm
To calculate the amount of nylon needed to make 50 tea bags in the shape of a triangular pyramid with dimensions of 40mm, 35mm, and 45mm, we first need to find the surface area of the triangular pyramid.
The surface area of a triangular pyramid can be calculated using the formula:
Surface Area = base area + 1/2 * perimeter * slant height
First, we need to calculate the base area of the triangular pyramid:
Base area = 1/2 * base perimeter * apothem
Base perimeter = 40 + 35 + 45 = 120mm
Apothem = height of the equilateral triangle = (sqrt(3)/2) * side length = (sqrt(3)/2) * 40 = 34.64mm
Base area = 1/2 * 120 * 34.64 = 2078.4mm^2
Next, we calculate the slant height of the triangular pyramid:
Slant height = sqrt((45/2)^2 + 40^2) = 45.89mm
Now we can calculate the surface area of the triangular pyramid:
Surface Area = 2078.4 + 1/2 * 120 * 45.89 = 4712.4mm^2
Since we need to make 50 tea bags, the total surface area of nylon needed is:
Total surface area = 50 * 4712.4 = 235620mm^2
Therefore, 235620mm^2 of nylon is needed to make 50 tea bags in the shape of a triangular pyramid with dimensions of 40mm, 35mm, and 45mm.