The mailing tube shown below is 36 in. long, 6 in. wide, and 5.2 in. deep. The bases are equilateral triangles. How much cardboard is used to make the tube?
To find out how much cardboard is used to make the mailing tube, we need to calculate the surface area of the tube.
The tube consists of two equilateral triangle bases and a rectangular side.
To calculate the surface area of the tube, we can follow these steps:
1. Calculate the surface area of the rectangular side:
The rectangular side has a height of 36 inches and a width equal to the perimeter of the equilateral triangle base, which is 6 inches. The surface area of a rectangle is given by the formula: Area = Length × Width. Therefore, the surface area of the rectangular side is 36 inches × 6 inches = 216 square inches.
2. Calculate the surface area of one equilateral triangle base:
The area of an equilateral triangle can be calculated using the formula: Area = (√3 / 4) × side^2, where side represents the length of one side of the triangle. Since the triangle is equilateral, all sides are equal. The side length can be found using the Pythagorean theorem: side = √(base^2 - (height/2)^2). In this case, the base and height of the triangle are both 6 inches. Plugging these values into the formula for the area, we can find the area of one equilateral triangle base.
3. Calculate the surface area of both triangle bases and the rectangular side:
Since there are two triangle bases and one rectangular side, we need to calculate the total surface area by adding them together: Total Surface Area = 2 × (Area of Triangle Base) + Area of Rectangular Side.
Using these calculations, we can find the amount of cardboard used to make the tube.