# 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?

(i) Edge of cube = 10 cm

Length (l) of box = 12.5 cm

Breadth (b) of box = 10 cm

Height (h) of box = 8 cm

Lateral surface area (Cubical box) = 4(edge)2

= 4(10 cm)2

= 400 cm2

Lateral surface area (Cuboidal box) = 2[lh + bh]

= [2(12.5 × 8 + 10 × 8)] cm2

= (2 × 180) cm2

= 360 cm2

Clearly, the lateral surface area of the cubical box is greater than the lateral surface area of the cuboidal box

Lateral surface area of cubical box − Lateral surface area of cuboidal box = 400 cm2 − 360 cm2 = 40 cm2

Therefore, the lateral surface area of the cubical box is greater than the lateral surface area of the cuboidal box by 40 cm2

(ii) Total surface area of cubical box = 6(edge)2

= 6(10 cm)2

= 600 cm2

Total surface area of cuboidal box = 2[lh + bh + lb]

= [2(12.5 × 8 + 10 × 8 + 12.5 × 10] cm2

= 610 cm2

Clearly, the total surface area of the cubical box is smaller than that of the cuboidal box

Total surface area of cuboidal box − Total surface area of cubical box = 610 cm2 – 600 cm2

= 10 cm2

Therefore, the total surface area of the cubical box is smaller than that of the cuboidal box by 10 cm2

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