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

Result

x =  0

Solution:

S=11 dm2 a=2 dm b=15 cm=15/10 dm=1.5 dm c=12 cm=12/10 dm=1.2 dm  S1=a b+2 c (a+b)=2 1.5+2 1.2 (2+1.5)=575=11.4 dm2  S1>S 11.4>11 x=0S=11 \ \text{dm}^2 \ \\ a=2 \ \text{dm} \ \\ b=15 \ cm=15 / 10 \ dm=1.5 \ dm \ \\ c=12 \ cm=12 / 10 \ dm=1.2 \ dm \ \\ \ \\ S_{1}=a \cdot \ b + 2 \cdot \ c \cdot \ (a+b)=2 \cdot \ 1.5 + 2 \cdot \ 1.2 \cdot \ (2+1.5)=\dfrac{ 57 }{ 5 }=11.4 \ \text{dm}^2 \ \\ \ \\ S_{1} > S \ \\ 11.4 > 11 \ \\ x=0



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