A candy bar box is in a shape of a triangular prism.
It shows 17 cm, 15cm, 16cm, 20cm, and 17cm.
Part A: Find the volume of the candy bar box. Show your work.
Part B: Find the surface area to approximate the amount of cardboard used to make the candy bar box. Show your work.
Part A:
To find the volume of a triangular prism, you need to multiply the area of the base (which is a triangle) by the height of the prism.
First, calculate the area of the base triangle using the formula: Area = (1/2) * base * height
Area = (1/2) * 17 cm * 15 cm
Area = (1/2) * 255
Area = 127.5 cm^2
Now, multiply the area of the base by the height of the prism to find the volume:
Volume = base area * height
Volume = 127.5 cm^2 * 20 cm
Volume = 2550 cm^3
Therefore, the volume of the candy bar box is 2550 cubic centimeters.
Part B:
To find the surface area of a triangular prism, you need to calculate the areas of all the faces and add them together.
First, calculate the area of the two triangular faces:
Area = (1/2) * base * height
Area = (1/2) * 17 cm * 15 cm
Area = (1/2) * 255
Area = 127.5 cm^2
Now, calculate the area of the three rectangular faces:
Face 1: 15 cm * 20 cm = 300 cm^2
Face 2: 16 cm * 20 cm = 320 cm^2
Face 3: 17 cm * 20 cm = 340 cm^2
Next, calculate the total surface area by adding up the areas of all faces:
Total surface area = 2 * triangular face area + 3 * rectangular face area
Total surface area = 2 * 127.5 cm^2 + 3 * (300 cm^2 + 320 cm^2 + 340 cm^2)
Total surface area = 255 cm^2 + 3 * 960 cm^2
Total surface area = 255 cm^2 + 2880 cm^2
Total surface area = 3135 cm^2
Therefore, the approximate amount of cardboard used to make the candy bar box is 3135 square centimeters.
make it shorter please
Part A:
Volume = base area * height
Volume = (1/2) * 17 cm * 15 cm * 20 cm
Volume = 2550 cm^3
Part B:
Surface area = 2 * triangle area + 3 * rectangle area
Surface area = 2 * (1/2) * 17 cm * 15 cm + 3 * (15 cm * 20 cm + 16 cm * 20 cm + 17 cm * 20 cm)
Surface area = 510 cm^2 + 3000 cm^2
Surface area = 3510 cm^2
Therefore, the candy bar box has a volume of 2550 cubic centimeters and the surface area is 3510 square centimeters.
make it look like a human wrote it
Sure!
Part A:
To find the volume of the candy bar box, we use the formula: Volume = base area * height.
First, we calculate the area of the base triangle: Area = (1/2) * base * height.
Area = (1/2) * 17 cm * 15 cm = 127.5 cm^2.
Then, we multiply the area of the base by the height of the prism: Volume = 127.5 cm^2 * 20 cm = 2550 cm^3.
Part B:
To find the surface area of the candy bar box, we calculate the areas of all faces and add them together.
The surface area is composed of 2 triangular faces and 3 rectangular faces.
After calculating all the areas, we add them up to find the total surface area.
Therefore, the candy bar box has a volume of 2550 cubic centimeters and the surface area is 3510 square centimeters.