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?

Given

Edge of a cube = 10cm

Length, l = 12.5 cm

Breadth, b = 10cm

Height, h = 8 cm

Find out

We have to find 

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

(i)

Lateral surface area of a cube = 4 * (edge)2

 = 4 * 102 cm2

 = 400 cm2

Lateral surface area of a cuboid = 2 (lh + bh)

= 2 (12.5 * 8 + 10 * 8) cm2

= 2 (100 + 80) cm2

= 360 cm2

So, the lateral surface area of the cubical box is greater than cuboidal box by (400 cm2 – 360 cm2) which is 40 cm2.

(ii) 

Total surface area of a cube = 6 * (edge)2

= 6 * 102 cm2

 = 600 cm2

Total surface area of cuboid = 2 (lb + bh + lh)

= 2 (12.5 * 10 + 10 * 8 + 12.5 * 8) cm2

= 2 (125 + 80 + 100) cm2

= 610 cm2

Therefore, the total surface area of the cuboidal box is greater than the cubical box by (610 cm2 – 600 cm2) which is 10 cm2.

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