A box of cereal measures 8 inches high and 2 inches deep. If all surfaces are made of cardboard and the total amount of overlapping cardboard in the box is 7 square inches, how much cardboard is used to make the cereal box?
The 3-dimensional box cannot be described by 2 dimensions.
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To determine the amount of cardboard used to make the cereal box, we need to find the surface area of all the sides and subtract the overlapping cardboard.
1. First, let's calculate the surface area of the front and back sides of the box. The dimensions for these sides are 8 inches high and 2 inches deep. So the surface area of each side is 8 inches * 2 inches = 16 square inches.
2. Next, let's calculate the surface area of the two smaller sides (left and right). The dimensions for these sides are 8 inches high and 2 inches deep. So the surface area of each side is 8 inches * 2 inches = 16 square inches.
3. Now, let's calculate the surface area of the top and bottom sides of the box. The dimensions for these sides are 2 inches deep and 2 inches wide. So the surface area of each side is 2 inches * 2 inches = 4 square inches.
4. To find the total surface area of the box, we add up the surface areas of all the sides: (16 square inches + 16 square inches) + (4 square inches + 4 square inches) = 40 square inches.
5. Finally, we need to subtract the overlapping cardboard, which is given as 7 square inches: 40 square inches - 7 square inches = 33 square inches.
Therefore, the amount of cardboard used to make the cereal box is 33 square inches.
To determine how much cardboard is used to make the cereal box, you need to calculate the total surface area of the box and subtract the overlapping area.
Step 1: Identify the surfaces of the box
A cereal box typically has six surfaces: a top, a bottom, two sides, a front, and a back.
Step 2: Calculate the surface area of each side
The top and bottom surfaces have the same dimensions, so you need to calculate the surface area of one and then multiply it by two.
Surface area of the top/bottom = length × width
In this case, the length and width are both the same, so you can use the dimensions provided. Each side measures 8 inches high and 2 inches deep, so the surface area of each side is:
Side surface area = height × depth
Step 3: Calculate the surface area of the front and back
The front and back surfaces have the same dimensions, so you need to calculate the surface area of one and then multiply it by two.
Surface area of the front/back = height × depth
Step 4: Calculate the total surface area of the box
To find the total surface area of the box, add up the surface area of all the sides.
Total surface area = 2 × (top/bottom surface area) + 2 × (side surface area) + 2 × (front/back surface area)
Step 5: Subtract the overlapping area
Subtract the given overlapping area from the total surface area to find the amount of cardboard used to make the cereal box.
Cardboard used = Total surface area - Overlapping area
Plug in the numbers and calculate to find the solution.