A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.
A triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm.
Part A: What is the height of the base? Show your work
To find the height of the base of the triangular prism, we can use the formula for the volume of a prism:
Volume = Base Area x Height
Given that the volume is 1,200 cubic centimeters and the base of the triangle is 10 cm and the sides of the triangle are 13 cm, the base area can be calculated as follows:
Base Area = (1/2) x base x height
Base Area = (1/2) x 10 cm x 13 cm
Base Area = 65 cm^2
Now we can plug the base area and volume into the formula to find the height:
1,200 cm^3 = 65 cm^2 x Height
Height = 1,200 cm^3 / 65 cm^2
Height = 18.46 cm
Therefore, the height of the base of the triangular prism is approximately 18.46 cm.
A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.
A triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm.
Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer.
To find the amount of cardboard used to make the candy box, we need to calculate the total surface area of the triangular prism. The total surface area of a triangular prism consists of the area of the two triangular bases and the three rectangular lateral faces.
1. The area of one triangular base:
Area = (1/2) x base x height
Area = (1/2) x 10 cm x 8.77 cm ≈ 43.85 cm^2
Since there are two triangular bases, the total area of the two bases is:
43.85 cm^2 x 2 = 87.70 cm^2
2. The area of the three rectangular lateral faces:
Area = perimeter of the triangle x height
Perimeter of the triangle = 10 cm + 13 cm + 13 cm = 36 cm
Area = 36 cm x 20 cm = 720 cm^2
Since there are three rectangular lateral faces, the total area of the three faces is:
720 cm^2 x 3 = 2160 cm^2
Now we can find the total surface area of the triangular prism:
Total Surface Area = 87.70 cm^2 + 2160 cm^2
Total Surface Area ≈ 2247.70 cm^2
Therefore, the approximate amount of cardboard used to make the candy box is approximately 2247.70 square centimeters.