Question

diana has gift box that is 11 inches long, 8 inches wide and 6 inchers she has a sheet of wrapping paper that is 4 feet long by 1 foot wide does she have enough wrapping paper to wrap the box? justify your anwser

Answer 1

For this problem we need the paper sand to be enough to cover the surface of the box.

now we calculate the surface area of the box finding the area of each face

Surface

frontal face and bottom

the area is

$\begin{gathered} A=6\times11 \\ A=66 \end{gathered}$

the area of frontal face and bottom is

$\begin{gathered} A=66+66 \\ A=132 \end{gathered}$

left and right face

the area is

$\begin{gathered} A=6\times8 \\ A=48 \end{gathered}$

area of both sides

$\begin{gathered} A=48+48 \\ A=96 \end{gathered}$

upper and lower face

$\begin{gathered} A=8\times11 \\ A=88 \end{gathered}$

and the are of both face is

$\begin{gathered} A=88+88 \\ A=176 \end{gathered}$

Total Surface is the sum of the area of all faces

$\begin{gathered} S=132+96+176 \\ S=404 \end{gathered}$

Total surface of the box is 404 squre inches

Area of the paper

first we change the feet per inches to do the comparison with the surface area of the bos

$\begin{gathered} 4ft\times12=48in \\ 1ft\times12=12in \end{gathered}$

the paper is

and the area of the paper is

$\begin{gathered} A=12\times48 \\ A=576 \end{gathered}$

the area of the paper is 576square inches

$576>404$

the are of the paper is greater than the suface area of the box, the paper will be enough