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Question

There are two cuboidal boxes as shown in the adjoining figure.

Which box requires the lesser amount of material to make?


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Solution

Step-1: Find the total surface area ofboxa as shown in the figure.

The total surface area ofboxa=2×(l×b+b×h+h×l) (As boxais in cuboidal shape )

Length, l=60cm

breadth, b=40cm ( As per the given boxadiagram )

Height, h=50cm

The total surface area ofboxa=2×(60×40+40×50+50×60)

The total surface area ofboxa=2×(2400+2000+3000)

The total surface area ofboxa=2×7400

The total surface area ofboxa=14,800cm2--------- (i)

Step-2: Find the total surface area ofboxb as shown in the figure.

The total surface area ofboxb=6×(side)2 (As boxbis in cubical shape )

Side, s=50cm ( As per the given boxbdiagram )

The total surface area ofboxb=6×(50)2

The total surface area ofboxb=6×2500

The total surface area ofboxb=15,000cm2--------- (ii)

From (i) and (ii), we can clearly see that total surface area of boxais lesser than boxb

Hence, boxarequires a lesser amount of material to make it.


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