Question

To determine the amount of wrapping paper needed for a rectangular box, Ryan finds the surface area of the box. How much wrapping paper is needed if the box measures 10 cm by 3 cm by 8 cm?220 cm2 of wrapping paper134 cm2 of wrapping paper268 cm2 of wrapping paper240 cm2 of wrapping paper

Answer 1

Let's draw a picture of our box:

So we need to find the area of the 6 rectangular faces, which can be grouped in 3 pairs:

Then, for rectangle 1, the area is

`\begin{gathered} A_1=\text{ base}* heigth \\ A_1=10*8 \\ A_1=80cm^2 \end{gathered}`

Simlarly, for rectangle 2, we have

`\begin{gathered} A_2=10*3 \\ A_2=30cm^2 \end{gathered}`

and for rectangle 3, we get

`\begin{gathered} A_3=3*8 \\ A_3=24cm^2 \end{gathered}`

Therefore, the surface area (S) of the box is given as

`S=2* A_1+2* A_2+2* A_3`

then, by substituting our above result into the last equation, we have

`S=2*80+2*30+2*24`

which gives

`\begin{gathered} S=160+60+48 \\ S=268cm^2 \end{gathered}`

Therefore, the answer is: 268 square centimeters of wrapping paper. (Option 3 from top to bottom)