A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. Which box has the greater lateral surface area and by how much?

(i) Lateral surface area of cube = 4(edge)² = 4(10)² = 400 cm²
Lateral surface area of cuboidal box = 2(lh + bh) = 2(12.5 × 8 + 10 × 8) = 2 × 180 = 360 cm²
∴ Lateral surface area of cubical box > Lateral surface area of cuboidal box
⇒ Difference: 400 - 360 cm² = 40 cm²
(ii) Total surface area of cubical box = 6(edge)² = 6(10)² = 600 cm²
Total surface area of cuboidal box = 2(lb + bh + lh) = 2(12.5 × 10 + 10 × 8 + 12.5 × 8) = 2(125 + 80 + 100) = 610 cm²
Total S.A of cuboidal box > cubical total S.A
Difference = 610 - 600 cm² = 10 cm²