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State true or false:

There are two cuboidal boxes as shown in the adjoining figure. Box (a) requires the lesser amount of material to make than box (b).

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Detailed Solution

It is given two cuboidal boxes as shown in the adjoining figure,
Question Image

Dimensions of cuboid (a);

l = 60 c m, b = 40 cm

and

h = 50 cm

Dimensions of cuboid (b);

l = 50 c m, b = 50

cm and

h = 50 cm

The Surface area of cuboid (a)

⇒ 2 × (l × b + b × h + h × l) ⇒ 2 × (60 × 40 + 40 × 50 + 50 × 60) ⇒ 2 × (2400 + 2000 + 3000) ⇒ 14800 cm 2

Calculate Surface area of cuboid (b)

⇒ 2 × (1 × b + b × h + h × l) ⇒ 2 × (50 × 50 + 50 × 50 + 50 × 50) ⇒ 2 × (2500 + 2500 + 2500) ⇒ 15000 cm 2

Comparing the equation, the surface area of cuboid (a) is less than the surface area of cuboid (b) .
That is, cuboid (a) requires less material to make than cuboid (b).
Given statement is true.
Hence, option (1) is correct.

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