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.

Share

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

Volume of the block of wood = 20×10×10 = 2000 cm

^{3}[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)r

^{2}h= (1/3)×(22/7)×5

^{2}×20= (22×25×20)/(3×7)

= 11000/21 cm

^{3}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 cm

^{3}Hence the volume of the remaining wood is 1476.19 cm

^{3}.