Question
Fran bought a box of cookies that matches the dimensions of the solid below. How many square units of cardboard were used to construct the box? If your solution is not a whole number, round to the nearest tenth. width=4mm length=3mm height=5.7mm height=4mm
Answers
GPT 3.5
To calculate the surface area of the box, we need to find the area of each of the six faces and add them together.
1. Top and bottom faces:
- Each of these faces has a length of 4 mm and width of 3 mm. So, the area of each is 4 mm * 3 mm = 12 square mm.
2. Front and back faces:
- Each of these faces has a length of 5.7 mm and width of 3 mm. So, the area of each is 5.7 mm * 3 mm = 17.1 square mm.
3. Left and right faces:
- Each of these faces has a length of 5.7 mm and height of 4 mm. So, the area of each is 5.7 mm * 4 mm = 22.8 square mm.
Now, add all the areas together to find the total surface area of the box:
Total surface area = 2(12) + 2(17.1) + 2(22.8)
Total surface area = 24 + 34.2 + 45.6
Total surface area = 103.8 square mm
Therefore, the box used approximately 103.8 square mm of cardboard to construct. Rounding to the nearest tenth, we get 103.8 square mm.
1. Top and bottom faces:
- Each of these faces has a length of 4 mm and width of 3 mm. So, the area of each is 4 mm * 3 mm = 12 square mm.
2. Front and back faces:
- Each of these faces has a length of 5.7 mm and width of 3 mm. So, the area of each is 5.7 mm * 3 mm = 17.1 square mm.
3. Left and right faces:
- Each of these faces has a length of 5.7 mm and height of 4 mm. So, the area of each is 5.7 mm * 4 mm = 22.8 square mm.
Now, add all the areas together to find the total surface area of the box:
Total surface area = 2(12) + 2(17.1) + 2(22.8)
Total surface area = 24 + 34.2 + 45.6
Total surface area = 103.8 square mm
Therefore, the box used approximately 103.8 square mm of cardboard to construct. Rounding to the nearest tenth, we get 103.8 square mm.