Answer:
a) Box1: 1 cm × 1 cm × 50 cm
Box2: 1 cm × 25 cm × 2 cm
Box3: 1 cm × 5 cm × 10 cm
Box4: 5 cm × 5 cm × 2 cm
b) Box 4 needs lees material. S=90cm²
c) I would recommend to use the 5 cm×5 cm×2cm box because it uses less material.
Step-by-step explanation:
a) The number 50 can be represented as:
50=1×1×50
50=1×5×10
50=1×25×2
50=5×5×2
Hence, these are all the possibilities of the dimensions of the boxes:
Box1: 1 cm × 1 cm × 50 cm
Box2: 1 cm × 25 cm × 2 cm
Box3: 1 cm × 5 cm × 10 cm
Box4: 5 cm × 5 cm × 2cm
b) [tex]S_{Box1}=2(1cm*1cm)+2(1cm*50cm)+2(50cm*1cm)=201 cm^2[/tex]
[tex]S_{Box2}=2(1cm*25cm)+2(25cm*2cm)+2(25cm*1cm)=200cm^2[/tex]
[tex]S_{Box3}=2(1cm*5cm)+2(5cm*10cm)+2(10cm*1cm)=130cm^2[/tex]
[tex]S_{Box4}=2(5cm*5cm)+2(5cm*2cm)+2(5cm*2cm)=90cm^2[/tex]
