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

(i) Which box has a smaller total surface area?

(ii) If each edge of the cube is doubled, how many times will its T.S.A increase?

Given: Edge of a cubical box = 10cm

Dimensions of cuboidal box:

Length(l) = 12.5cm

Breadth(b) = 10cm

Height(h) = 8cm

(i) Total Surface Area of a cube = 6 (side of cube)²

= 6(10)²

= 6 × 10 × 10

= 600 cm²

Total Surface Area of a Cuboidal box = 2{(l × b) + (b × h) + (h × l)}

= 2 (12.5 × 10 + 10 × 8 + 8 × 12.5)

= 2 (125 + 80 + 100)

= 2 (305)

= 610 cm²

(ii) Given: If each edge of a cube is doubled then a’= 2a = 2 × 10 = 20cm

New Total Surface Area of a cube = 6(a’)²

= 6(20)²

=2400 cm²

So, new total surface area is 4 times the old total surface area.