Question

The difference between the outer lateral surface area and inner lateral surface area of a cylindrical metal pipe 28 cm long is 176 cm². Find the outer and the inner radii of the pipe, if the pipe is made of 352 cm³ of metal.

Explain with complete calculations & justifications.

Points : 20 ☺

Answer 1

Suppose r be the inner radius and r' be the outer .
We are given volume of metal by using which pipe is made .
volume of metal used(say u ) = 352 cm³

we know that Volume of a cylinder given by :
Πr²h
where h is length of cylinder and r is radius of cross section.
Then,
The volume of pipe (say V) = Πr'²h
The volume of Cylindrical cavity inside the pipe(say v ) = Πr²h
Then,
u = V-v
352 = Π(r'²-r²)h
( h= 28)
352 = Π (r'²-r²)×28
solving it we get the relation :
r'² -r² = 4
using[ a²-b² = (a+b)(a-b)] we get :
( r'-r)(r'+r) = 4 ........................ (1)
___________________
Further ,
Given the difference in lateral Surface area = 176 cm².
we know that lateral surface area of a cylinder is given by :
2Πrh
The outer LSA of pipe = 2Πr'h
The inner LSA of pipe = 2Πrh
then,
176 = 2Π(r'-r )×28 ,
Solving it we get our second equation ;
r'-r = 1.............(2)
___________________
using (2) replace (r'-r) from (1) ;
we get;
(1)(r'+r) = 4
r'+r=4
=> r' = 4-r ..............(3)
using value of r' from (3) and using in (2) we get;
(4-r)-r = 1
=> r = 3/2 cm
and finally using the above value of r in (3) we get :
r' = 4-3/2 = 5/2 cm
______________________
INNER RADIUS = 3/2cm
OUTER RADIUS = 5/2 cm
_______________________
Hope it hepls !

Answer 2

this may help you solving the answer