Box wrapping paper

Mother and daughter Susan are wrapping presents for father. Matt has a cube-shaped box with dimensions of 9 cm, 3 cm, and 7 cm, and Susan has a box in the shape of a cube with an edge length of 3 cm. How many square cm of wrapping paper will they use in total if they need 20% more for overlap?

Final Answer:

S =  331.2 cm²

Step-by-step explanation:

$$\begin{gathered} a=9\text{cm} \\ b=3\text{cm} \\ c=7\text{cm} \\ x=3\text{cm} \\ {S}_1=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (9\cdot 3+3\cdot 7+7\cdot 9)=222{\text{cm}}^2 \\ {S}_2=6\cdot x^2=6\cdot 3^2=54{\text{cm}}^2 \\ q=100\%+20\%=1+\frac{20}{100}=1.2 \\ S=q\cdot S_1+q\cdot S_2=1.2\cdot 222+1.2\cdot 54=331.2{\text{cm}}^2 \end{gathered}$$

Try another example