Question
4.
(05.05 HC)
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. (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)
(05.05 HC)
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. (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)
Answers
GPT 3.5
Part A:
To find the height of the base, we need to use the formula for the volume of a triangular prism:
Volume = (1/2) * base * height * length
Plugging in the values we know:
1,200 = (1/2) * 10 * h * 20
1,200 = 100h
h = 1,200 / 100 = 12 cm
Therefore, the height of the base is 12 cm.
Part B:
To find the amount of cardboard used to make the candy box, we need to calculate the surface area of the triangular prism. The surface area of a triangular prism can be calculated by finding the area of the two triangular bases and the three rectangular faces and adding them together.
Area of a triangular base = (1/2) * base * height
Area of one triangular base = (1/2) * 10 * 12 = 60 cm^2
Area of both triangular bases = 2 * 60 = 120 cm^2
Area of a rectangular face = base * height
Area of one rectangular face = 10 * 20 = 200 cm^2
Area of all three rectangular faces = 3 * 200 = 600 cm^2
Total surface area = 120 + 600 = 720 cm^2
Therefore, approximately 720 square centimeters of cardboard would be used to make the candy box.
To find the height of the base, we need to use the formula for the volume of a triangular prism:
Volume = (1/2) * base * height * length
Plugging in the values we know:
1,200 = (1/2) * 10 * h * 20
1,200 = 100h
h = 1,200 / 100 = 12 cm
Therefore, the height of the base is 12 cm.
Part B:
To find the amount of cardboard used to make the candy box, we need to calculate the surface area of the triangular prism. The surface area of a triangular prism can be calculated by finding the area of the two triangular bases and the three rectangular faces and adding them together.
Area of a triangular base = (1/2) * base * height
Area of one triangular base = (1/2) * 10 * 12 = 60 cm^2
Area of both triangular bases = 2 * 60 = 120 cm^2
Area of a rectangular face = base * height
Area of one rectangular face = 10 * 20 = 200 cm^2
Area of all three rectangular faces = 3 * 200 = 600 cm^2
Total surface area = 120 + 600 = 720 cm^2
Therefore, approximately 720 square centimeters of cardboard would be used to make the candy box.