Answer :
To find the total surface area of the box that needs to be covered with paper, we use the formula for the surface area of a rectangular prism. The surface area [tex]S[/tex] of a rectangular box can be calculated using the formula:
[tex]S = 2(lw + lh + wh)[/tex]
Where:
- [tex]l[/tex] is the length of the box
- [tex]w[/tex] is the width of the box
- [tex]h[/tex] is the height of the box
In this case:
- [tex]l = 38.8[/tex] cm
- [tex]w = 27.5[/tex] cm
- [tex]h = 30[/tex] cm
Substitute these values into the formula:
[tex]S = 2((38.8 \times 27.5) + (38.8 \times 30) + (27.5 \times 30))[/tex]
Let's calculate each component step-by-step:
[tex]1. lw = 38.8 \times 27.5 = 1067[/tex] square centimeters
[tex]2. lh = 38.8 \times 30 = 1164[/tex] square centimeters
[tex]3. wh = 27.5 \times 30 = 825[/tex] square centimeters
Add these areas:
[tex]lw + lh + wh = 1067 + 1164 + 825 = 3056[/tex] square centimeters
Multiply by 2 (since each pair of opposite sides is equal):
[tex]S = 2 \times 3056 = 6112[/tex] square centimeters
Thus, the total surface area of the paper needed to wrap the gift box is [tex]6112[/tex] square centimeters.
