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A cone of maximum volume is curved out of a block of wood of size 20 cm x 10 cm x 10 cm. Find the volume of the remaining wood.

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M.L Aggarwal book Important Question of class 10 chapter Based on Mensuration for ICSE BOARD.
A cone of maximum volume is curved out of a block of wood of given size. Find the volume of the remaining wood.
This is the Question Number 04, Exercise 17.4 of M.L Aggarwal.

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1 Answer

  1. ML Aggarwal Sol Class 10 Maths chapter 17-21

    Given dimensions of the block of wood = 20 cm × 10 cm× 10 cm

    Volume of the block of wood = 20×10×10 = 2000 cm3 [Volume = lbh]

    Diameter of the cone, d = 10 cm

    Radius of the cone , r = d/2 = 10/2 = 5 cm

    Height of the cone, h = 20 cm

    Volume of the cone = (1/3)r2h

    = (1/3)×(22/7)×52×20

    = (22×25×20)/(3×7)

    = 11000/21 cm3

    Volume of the remaining wood = Volume of block of wood – Volume of cone

    = 2000-11000/21

    = (21×2000-11000)/21

    = (42000-11000)/21

    = 31000/21

    = 1476.19 cm3

    Hence the volume of the remaining wood is 1476.19 cm3.

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