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.
Deepak BoraNewbie
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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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.