Given info:-If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height.
Find the ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder ?
Explanation:-
Let the radius of the right circular cylinder be r units
Let the radius of the right circular cylinder be h units
Curved Surface Area of the original right circular cylinder = 2Ï€rh sq.units ----(i)
If the radius of the right circular cylinder is doubled then the radius of the new cylinder = 2r units
The height of the new right circular cylinder
= (1/4)×h units
⇛ h/4 units
Curved Surface Area of the new cylinder
= 2Ï€(2r)(h/4) sq.units
⇛ 4πrh/4 sq.units
⇛ πrh sq.units --------(ii)
The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder
⇛ πrh : 2πrh
⇛ πrh / 2πrh
⇛ 1/2
⇛ 1:2
Therefore the ratio = 1:2
The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder is 1:2
