From a solid circular cylinder with height 12 cm and radius of the base 5 cm, a right circular cone of the same height and the same base radius is removed find the volume and total surface area of the remaing solid . [User `pi = 3.14 ]`

Explanation

Radius of each of the cylinder and cone , r= 5 cm
Height of each of the cylinder and cone h= 12 cm
Slant height of the cone
`l sqrt(r^2+h^2)=sqrt(5^2+(12)^2)`
`=sqrt(169)cm` = 13 m
Volume of the remaining solid
volume of the cylinder - volume of the cone
`pi r^2h-1/3pi r^2 h= 2/3pi r^2 h `
`(2/3xx3.14 xx 5xx5 xx12)cm^3=628 cm^3`
Total surface area of the reamining solid
= curved suface area of the cylinder + curved suface area of the cone + area of the upper circular face of the cylinder
`2pirh+pi rl+pir^2=pir(2h+l+r)`
`=[3.14 xx 5xx(2 xx 12 +13 + 5 )]cm^2`
`=(3.14 xx 5 xx 42)cm^2=659.cm^2`
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