box of cereal measures 10 in .wide.12in . high, 3in deep .all surfaces made of cardboard and total overlapping cardboard in the box is 7in squared , how much cardboard is used to make a cereal box including the amount of overlapping parts ?
The area of all the exposed faces is
2(10*12 + 10*3 + 12*3) = 372 in^2
add to that the 7 in^2 of overlap.
To calculate the amount of cardboard used to make a cereal box, including the overlapping parts, you need to find the area of each individual surface and then add them up.
First, let's determine the areas of the surfaces:
The front and back surfaces are both 10 inches wide and 12 inches high, so their areas are:
Front/Back Area = 10 in * 12 in = 120 in²
The two side surfaces are both 3 inches deep and 12 inches high, so their areas are:
Side Area = 3 in * 12 in = 36 in²
The top surface is 10 inches wide and 3 inches deep, so its area is:
Top Area = 10 in * 3 in = 30 in²
Now, to account for the overlapping parts, subtract the overlapping area of 7 square inches:
Total Area (excluding overlapping parts) = Front/Back Area + 2 * Side Area + Top Area = 120 in² + 2 * 36 in² + 30 in² = 228 in²
However, we need to add the overlapping area to get the total amount of cardboard used for the cereal box:
Total Cardboard Area = Total Area (excluding overlapping parts) + Overlapping Area = 228 in² + 7 in² = 235 in²
Therefore, the total amount of cardboard used, including the overlapping parts, to make the cereal box is 235 square inches.