 # ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.4 in Chapter 17 - Mensuration

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.

Solution:

Volume of the remaining wood can be calculated using the difference between the volume of cuboidal block of wood and volume of cone. 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)π 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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