What changes in curved surface area of a right circular cone will be occured if its radius of base and height is doubled ?

Explanation

Let the radius of base , height and slant height of the right circular cone be r unit , h unit and l unit respectively.
`therefore l = sqrt(h^2+r^2)` ..............(1)
Now if the curved surface area of the cone be A sq-unit , then
`A = pi r l ` ...................(2)
Also , if the radius of base and the height of the cone be doubled , then lest the slant height of it be `l_1` units.
`therefore l_1=sqrt((2r)^2+(2h)^2)=sqrt(4r^2+4h^2)=sqrt(4(r^2+h^2))=2sqrt(h^2+r^2)=2l ` [by (1) ].................(3)
In this case , if the curved surface area be `A_1` sq-unit , then
`A_1=pi xx 2r xxl_1= pi xx 2r xx2l ` [by (3)] `=4pi r l = 4A` [by (2) ].
Hence if the radius of base and height of a right circular cone be doubled , then the curved surface area becomes 4 times of its previous curved surface area.