Question

from a cube of edge 14 cm a cone of maximum size is carved out. find the volume of the remaining material

Answer 1

Solution : The cone of maximum size that is carved out from a cube of edge 14 cmwill be of base radius 7 cm and the height 14 cm.Surface area of the cone = πrl + πr2= 2 2 22 227 7 147 7× × + + (7)2= ( ) 22 7 245 154 (154 5 154)cm2 154 5 1 cm27× × + = + = +Surface area of the cube = 6 × (14)2 = 6 × 196 = 1176 cm2So, surface area of the remaining solid left out after the cone is carved out= (1176 –154 + 154 5 )cm2 = (1022 + 154 5 ) cm2.