A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

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A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

(i) Which box has the greater lateral surface area and by how much?

(ii) Which box has the smaller total surface area and by how much?

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Here, a = 10 cm, l = 12.5 cm, b = 10 cm, h = 8 cm

(i) Lateral surface area of the cubical box = 4a2

= 4 × (10)2 cm2 = 400 cm

Lateral surface area of the cuboidal box = 2h (l + b)

= 2 × 8 (12.5 + 10) cm

= 16 × 22.5 cm2 = 360 cm

Difference in the lateral surface areas of the two boxes

= (400 – 360) cm2 = 40 cm2

Hence, the cubical box has greater lateral surface area by 40 cm2. Ans.

(ii) Total surface area of the cubical box = 6a2

= 6 × (10)2 cm2 = 600 cm2

Total surface area of the cuboidal box = 2(lb + bh + hl)

= 2(12.5 × 10 + 10 × 8 + 8 × 12.5) cm2

= 2(125 + 80 + 100) cm2

= 2 × 305 cm2 = 610 cm2

Difference in the total surface areas of the two boxes = (610 – 600) cm

= 10 cm2

Hence, the cubical box has smaller total surface area by 10 cm2 Ans