Question

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?

Answer 1

(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 of cubical box = 4(edge)²

= 4(10 cm)²

= 400 cm²

Lateral surface area of 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.