There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
(a) Given: Length of cuboidal box (l) = 60 cm
Breadth of cuboidal box (b) = 40 cm
Height of cuboidal box (h) = 50 cm
∴ Total surface area of cuboidal box = 2 (lb + bh + hl)
= 2 (60 × 40 + 40 × 50 + 50 × 60)
= 2 (2400 + 2000 + 3000)
= 2 × 7400 = 14800 cm2
(b) Given: Length of cubical box (l) = 50 cm
Total surface area of cubical box= 6l2
= 6 × 502
= 6 × 2500
= 15000 cm2
Hence cuboidal box (a) requires the lesser amount of material to make since surface area of box (a) is less than that of box (b).
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