a log of wood is in the shape of a cylinder of radius 1 ft and height 8 ft is cut all around to form a bigest cubiod. what volume of cylinder removed?

Dear Student,
Please find below the solution to the asked query:

For cylinder we have:RadiusR=1 ftHeightH=8 ftVolumeV1=πR2H=π×1×8=8π ft3Now as we are looking for biggest cuboid, hence height of cuboid should beequal to height of cylinder.Height of cuboidh=8 ftNow base should form a square because area of rectangle is maximum when it is a square.Again as as we are looking for biggest cuboid, henceDiagonal of Square=Diameter of CylinderIf a is length of side of square base, then we have:a2=2Ra2=2×1a=2 ftVolume of cuboidV2=a×a×h=2×2×8=16 ft3Volume of cylinder removed=V2-V1=8π-16=8π-2Volume of cylinder removed=8π-2 ft3

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