A candy bar box is in the shape of a triangular prism. The volume of the box is 2,400 cubic centimeters.
A triangular prism is shown with base of triangle labeled 16 cm, sides of triangles labeled 17 cm, and length of the box equal to 20 cm.
Part A: What is the height of the base? Show your work. (5 points)
Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)
Part A:
To find the height of the base of the triangular prism, we can use the formula for the volume of a triangular prism:
Volume = (1/2) * base * height * length
Substitute the given values:
2,400 = (1/2) * 16 * height * 20
2,400 = 160 * height
height = 2,400 / 160
height = 15 cm
Therefore, the height of the base of the triangular prism is 15 cm.
Part B:
To find the amount of cardboard used to make the candy box, we need to find the total surface area of the box. The surface area of a triangular prism can be calculated by adding the areas of the two triangular bases and the three rectangular sides.
The area of the triangular base can be calculated using the formula for the area of a triangle:
Area = (1/2) * base * height
Substitute the given values:
Area = (1/2) * 16 * 15
Area = 120 cm^2
Since there are two triangular bases, the total area for the bases is:
2 * 120 = 240 cm^2
The area of each rectangular side is the base of the triangle multiplied by the length of the box:
Area = base * length
Area = 16 * 20
Area = 320 cm^2
Since there are three rectangular sides, the total area for the sides is:
3 * 320 = 960 cm^2
Therefore, the approximate amount of cardboard used to make the candy box is:
240 (triangular bases) + 960 (rectangular sides) = 1,200 cm^2
So, the approximate amount of cardboard used to make the candy box is 1,200 cm^2.