The adjoining figure shows a cuboidal block of wood through which a circular cylindrical hole of the biggest size is drilled. Find the volume of the wood left in the block.
The adjoining figure shows a cuboidal block of wood through which a circular cylindrical hole of the biggest size is drilled. Find the volume of the wood left in the block.

Solution:

Given diameter of the hole, d = 30 cm

radius of the hole, r = d/2 = 30/2 = 15 cm

Height of the cylindrical hole, h = 70 cm

Volume of the cuboidal block = lbh

= 70×30×30

= 63000 cm3

Volume of cylindrical hole = r2h

= (22/7)×152×70

= 22×225×10

= 49500 cm3

Volume of the wood left in the block = 63000-49500 = 13500 cm3

Hence the volume of the wood left in the block is 13500 cm3.