A cubical box has each edge 10 cm and another cuboidal box is 12.5cm 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?

Solution:

From the question statement, we have

Edge of a cube = 10cm

Length, l = 12.5 cm

Breadth, b = 10cm

Height, h = 8 cm

(i) Find the lateral surface area for both the figures

Lateral surface area of cubical box = 4 (edge)2

= 4(10)2

= 400 cm2 …(1)

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

= [2(12.5×8+10×8)]

= (2×180) = 360

Therefore, Lateral surface area of cuboidal box is 360 cm2. …(2)

From (1) and (2), lateral surface area of the cubical box is more than the lateral surface area of the cuboidal box. The difference between both the lateral surfaces is, 40 cm2.

(Lateral surface area of cubical box – Lateral surface area of cuboidal box=400cm2–360cm2 = 40 cm2)

(ii) Find the total surface area for both the figures

The total surface area of the cubical box = 6(edge)2 = 6(10 cm)2 = 600 cm2…(3)

Total surface area of cuboidal box

= 2[lh+bh+lb]

= [2(12.5×8+10×8+12.5×100)]

= 610

This implies, Total surface area of cuboidal box is 610 cm2..(4)

From (3) and (4), the total surface area of the cubical box is smaller than that of the cuboidal box. And their difference is 10cm2.

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