The volume of a right circular cone is `410(2)/(3)c c`. If the radius of the base of the cone be 14 cm , then what will be the curved surface area of the cone ?

Explanation

Let the height of the cone be h cm.
The radius of the cone `=14 cm`.
`therefore` the volume of the cone `=(1)/(3)xx(22)/(7)xx14^2xxh c c` .
As per question , `(1)/(3)xx(22)/(7)xx14^2xxh=410 (2)/(3) or , (22)/(3)xx28h=(1232)/(3)or , h= (1232xx3)/(3xx22xx28)or, h=2`
`therefore` the height of the cone `=2cm`.
`therefore` the salnt height of the cone `=sqrt((14)^2+(2)^2)cm=sqrt(200)cm=sqrt(100xx2)cm=10sqrt(2)cm`
`therefore` the curved surface area of the cone `= (22)/(7)xx14xx10sqrt(2)sq-cm=440sqrt(2)sq-cm`
Hence the required curved surface of the cone `=440sqrt(2) sq-cm`.