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Question

Which among the following will have the largest value?


A

Surface area of a cube with side 6 cm.

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B

Surface area of a cuboid with l=7 cm, b=6 cm and h=5 cm.

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C

Surface area of the walls of a cube having side 8 cm.

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D

Surface area of the walls of a cuboid having l=10 cm, b=5 cm and h=6 cm.

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Solution

The correct option is C

Surface area of the walls of a cube having side 8 cm.


We know, TSA of a cube of side 'a'=6a2
And, TSA of a cuboid of dimensions l×b×h=2(lb+bh+hl)

So, surface area of a cube with side 6 cm
=6×(6)2=216 cm2

Surface area of a cuboid with length l=7 cm, breadth b=6 cm and height h=5 cm
=2(lb+bh+hl)
=2(7×6+6×5+5×7)
=2(42+30+35)
=2×107=214 cm2

'To find the surface area of the walls of a three dimensional solid' means 'to find its lateral surface area'.

We know, LSA of a cube of side 'a'=4a2
And, LSA of a cuboid of dimensions l×b×h=2(lh+bh)

So, surface area of the walls of a cube having side 8 cm
=4×(8)2
=4×64=256 cm2

Surface area of the walls of a cuboid having length l=10 cm, breadth b=5 cm and height h=6 cm
=2(bh+hl)
=2(5×6+6×10)
=2(30+60)
=2×90=180 cm2

Surface area of the walls of a cube having side 8 cm has the largest value among the give options.


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