Paper box

Calculate whether 11 dm² of paper is sufficient for gluing a box without a lid with bottom dimensions of 2 dm and 15 cm and 12 cm high. Write result as: 0 = No, 1 = Yes

Correct answer:

x =  0

Step-by-step explanation:

$$\begin{gathered} S=11{\text{dm}}^2 \\ a=2\text{ dm } \\ b=15\text{ cm}\to \text{ dm}=15\mathrm{/}10\text{ dm}=1.5\text{ dm } \\ c=12\text{ cm}\to \text{ dm}=12\mathrm{/}10\text{ dm}=1.2\text{ dm } \\ {S}_1=a\cdot b+2\cdot c\cdot (a+b)=2\cdot 1.5+2\cdot 1.2\cdot (2+1.5)={\displaystyle \frac{57}{5}}=11\frac{2}{5}=11.4{\text{dm}}^2 \\ {S}_1>S \\ 11.4>11 \\ x=0=0 \end{gathered}$$

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