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

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 cm² 

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

= 2 × 8 (12.5 + 10) cm² 

= 16 × 22.5 cm2 = 360 cm² 

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) cm² 

= 10 cm² 

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