Milk cartons

Monica measured the dimensions of two different milk cartons. One had dimensions of 9*5.8*19.6 cm, the other 9.4*6.3*17.3 cm. She wanted to see if less material was used to make a particular box. Check it out and find out what percentage of material is saved.
(We will neglect the material for foundation and gluing)

Final Answer:

p =  3.461 %

Step-by-step explanation:

$$\begin{gathered} a=9\text{cm} \\ b=5.8\text{cm} \\ c=19.6\text{cm} \\ x=9.4\text{cm} \\ y=6.3\text{cm} \\ z=17.3\text{cm} \\ {V}_1=a\cdot b\cdot c=9\cdot 5.8\cdot 19.6=\frac{25578}{25}=1023.12{\text{cm}}^3 \\ {V}_2=x\cdot y\cdot z=9.4\cdot 6.3\cdot 17.3=1024.506{\text{cm}}^3 \\ {V}_1\approx V_2\approx 1liter \\ {S}_1=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (9\cdot 5.8+5.8\cdot 19.6+19.6\cdot 9)=\frac{17114}{25}=684.56{\text{cm}}^2 \\ {S}_2=2\cdot (x\cdot y+y\cdot z+z\cdot x)=2\cdot (9.4\cdot 6.3+6.3\cdot 17.3+17.3\cdot 9.4)=\frac{33083}{50}=661.66{\text{cm}}^2 \\ p=100\cdot \frac{S_1-S_2}{S_2}=100\cdot \frac{684.56-661.66}{661.66}=3.461\% \end{gathered}$$

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