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A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. Which box has a smaller total surface area and by how much?

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Cubical box by 10

c m 2

Cuboidal box by 15

c m 2

Both are equal

None of the above

answer is A.

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Detailed Solution

Given, a cubical box of edge

a = 10 c m

,
And a cuboidal box of length=12.5 cm, height=8 cm, breadth=10 cm.
We know, total Surface area of the cube,

S = 6 a 2

where 'a' = side.

⇒ S = 6 (10) 2

⇒ 600 c m 2

For cuboidal box,

l = 12.5 c m

b = 10 c m

h = 8 c m

Total surface area of the cuboidal box,

S (c) = 2 (l b + b h + h l)

S (c) = 2 (12.5 × 10 + 10 × 8 + 8 × 12.5)

⇒ 610 c m 2

So, the total surface area of the cubical box is smaller than the cuboidal box by

⇒

610-600

⇒

c m 2

Therefore, the correct option is 1.

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