Question

A cylindrical pencil is sharpened to produce a perfect cone at one end with no over all loss of its height .The diameter of pencil is 1cm and the length of conical portion is 2cm calculate the volume of the peels give ur answer correct to two places if it is in decimal (use pie =335/113

Answer 1

A cylindrical pencil is sharpened to produce a perfect cone at one end with no loss in the total length of the pencil. Amount of shaving in pencil = Volume of cylindrical part with height 2 cm - Volume of conical portion of pencil

We know Volume of cylinder = πr2hHere we take Diameter = 1 cm , So radius r = 0.5 cmAndheight h = 2 cmSo,Volume of cylindrical part with height

2 cm = 227 × 0.5 × 0. 5 × 2 = 117 = 1.57 cm3AndWe know Volume of Cone = πr2h3

So,Volume of conical portion of pencil = 227 × 0.5 × 0. 5 × 2 3= 1121 = 0.52 cm3

Volume of shaving=(1.57-0.53)cc

=1.05cc