The difference between outside and inside surfaces of a cylindrical metallic pipe 14cm long is `44\ c m^2dot` If the pipe is made 99 cu centimetres of metal, find the outer and inner radii of the pipe.

Explanation

Let `r` and `R` be the inner and outer radius of the cylindrical metallic pipe respectively.
`h` be the height of the metallic pipe`=14 cm`
Difference between the Curved surface area of the outer cylinder and Curved surface area of the inner cylinder`=2piR-2pirh`.
Given that difference between the outside and inside curved surface area of cylinder is `44cm^2`.
`⇒2pih(R-r)=44`
`⇒44/7xx14(R-r)=44`
`⇒R-r=1/2=0.5` ----------(1)
Given the pipe is made up of `99` cubic cm of metal so that
Volume of cylindrical metallic pipe`=piR^2h-pir^2h`.
`⇒22/7xx14 (R^2-r^2)=99 cm3`
`⇒44xx(R^2-r^2)= 99`
`⇒(R^2-r^2)=9/4=2.25`
`⇒(R-r)(R+r)=2.25`
`=(0.5)×(R + r) = 2.25`
`R + r = 2.25/0.5= 4.5`
`R + r = 4.5` ------------ (2)
Adding (1) and (2) we get
`2R=4.5+0.5=5`
`∴R=2.5cm` and `r=2cm`
`∴` Outer side radius `R=2.5cm` and inner side radius `r=2cm`.