Question

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

Answer 1

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Answer 2

Answer with step-by-step-explanation:

(i) Let the total surface areas of the cubical and cuboidal boxes be S₁ and S₂ respectively. Then,

S₁ = 6(edge)²

S₁ = 6 × 10² cm²

S₁ = 6 × 100 cm²

S₁ = 600 cm²

and, S₂ = 2(12.5×10 + 10×8 + 8×12.5) cm²

S₂ = 2( 125 + 80 + 100 ) cm²

S₂ = 610 cm²

Hence, S₂ - S₁ = 610 - 600 = 10 cm²

Thus, the cuboidal box has greater total surface area and is greater by 10 cm².

(ii) Let total surface areas of the cubical and cuboidal boxes be L₁ and L₂ respectively. Then,

L₁ = 4(edge)²

L₁ = 4 (10)² cm²

L₁ = 4 × 100 cm²

L₁ = 400 cm²

and, L₂ = 2(l + b) × h

L₂ = 2(12.5 + 10) × 8 cm²

L₂ = 2 × 22.5 × 8 cm²

L₂ = 360 cm²

Thus, the cuboidal boxes larger lateral surface area and is greater by 40 cm².