The 2005 world record for the longest sandwich is 3.6 meters with a width of 3.6 meters and a thickness of 0.44 meters. If you cut the sandwich in half diagonally, it would create a triangular prism with a hypotenuse of 5.1 meters. Apply the technique of using nets to find the surface area.(1 point)
Responses
A: 18.37 m2
B: 12.98 m2
C: 16.22 m2
D: 14.63 m2
D: 14.63 m2
To find the surface area of the triangular prism created by cutting the sandwich in half diagonally, we can use the concept of nets.
A net is a 2D representation of a 3D shape that can be unfolded to determine its surface area. In this case, the triangular prism can be unfolded into three rectangles.
The formula to find the surface area of a rectangular prism is: Surface Area = 2 * (length * width + length * height + width * height).
In this case, since we are dealing with a triangular prism, one of the rectangles will have dimensions based on the hypotenuse of the triangle.
First, let's calculate the dimensions of the triangular prism:
- Length: The length is the same as the original length of the sandwich, which is 3.6 meters.
- Width: The width is the same as the original width of the sandwich, which is 3.6 meters.
- Height: The height is the same as the original thickness of the sandwich, which is 0.44 meters.
- Hypotenuse: The hypotenuse of the triangle is given as 5.1 meters.
Calculating the surface area:
- The first rectangle (which includes the hypotenuse) has dimensions of 5.1m (hypotenuse) x 3.6m (width).
- The second rectangle (end face) has dimensions of 3.6m (length) x 0.44m (height).
- The third rectangle (side face) has dimensions of 3.6m (length) x 0.44m (height).
Using the formula mentioned above, we can calculate the surface area:
Surface Area = 2 * (5.1 * 3.6 + 5.1 * 0.44 + 3.6 * 0.44)
Calculating this expression, we find that the surface area is approximately 18.37 square meters.
Therefore, the correct answer is A: 18.37 m2.