From a wooden cubical block of edge 7 cm , the largest paossible right conical piece is cut out whose base is on one of the faces of the cube. Calculate .
(i) the volume of the wood left in the block and
the total surface area of the block left (Taken `pi=(22)/(7)`

Explanation

Initial volume of the block =`a^(3)=7^(3)=cm^(3)`
The base of the largest cone will touch the sides of the base of the cube and the height will be equal to the length of an edge of the cube.
For the coine r=3.5 cm and h=7 cm
(i) the volume of the coine =`(1)/(3)pir^(2)h =(pi)/(3).((7)/(2))^(2).7cm^(3)`
volume of the wood left=`{(7^(3)-(1)/(3).(22)/(7).((7)/(2))^(2).4)}cm^(3)`

`=(7^(3))-(11xx7^(2))/(3xx2)cm^(3)=7^(2)(7-(11)/(6))cm^(3)`
`=(49xx31)/(6)cm^(3)=(1519)/(6)cm^(3)=253(1)/(6)cm^(3)`
(ii) The totl surface area of the wood left
=Totl surface area of the cube -Area of the base of the cone +curved surface area of the cone.
`=6a^(2)-pir^(2)+pirl`
`={(6xx7^(2)-(22))/(2).((7)/(22)^(2))+(22)/(7).(7)/(2).sqrt(7^(2)+(7)/(2)^(2))}cm^(2)`
`=(6xx49-(11xx7)/(2)+11.7.(sqrt(5))/(2)cm^(2)={(294+(77)/(2)(sqrt(5))-1)}cm^(2)`
=`(294+(77)/(2)xx1.24)cm^(2)=341.74 cm^(2)`