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Question

Visualise the area of a cuboid.


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Solution

Step 1: Drawing the figure

Let l,b and h be the length, breadth, and height of a cuboid respectively.

According to the figure, we have,

AB=CD=EF=GH=lBC=AD=EH=FG=bCG=BF=AE=DH=h

Step 2: Finding the curved surface area

The curved surface area (CSA) of a cuboid is the sum of areas of all its rectangular faces excluding the top and the bottom face i.e. area of four faces except top and bottom face.Lateralsurfaceareaofthecuboid=AreaoffaceADHE+AreaoffaceBCGF+AreaoffaceABFE+AreaoffaceDCGH=(AD×DH)+(BC×CG)+(AB×BF)+(CD×BC)=(b×h)+(b×h)+(l×h)+(l×h)=2(b×h)+2(l×h)

Hence, Lateral surface area of the cuboid=2h(l+b)sq.units

Step 3: Finding the total surface area

The total surface area (TSA) of a cuboid is the sum of areas of all its rectangular faces.

Area of face EFGH=AreaoffaceABCD=(l×b)

Area of face BFGC=AreaoffaceAEHD=(b×h)

Area of face DHGC=AreaoffaceABFE=(l×h)

Totalsurfaceareaofacuboid=Sumoftheareasofallits6rectangularfaces=Areaof(ABCD+EFGH+BFGC+AEHD+DHGC+ABFE)=(l×b)+(l×b)+(b×h)+(b×h)+(l×h)+(l×h)=2lb+2bh+2hl

Hence, Total surface area of a cuboid=2(lb+bh+hl)sq.units


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