Question

THE T.S.A OF A SOLID CYLINDER IS 462CM ITS C.S.A IS ONE THIRD OF T.S.A FIND THE VOL. OF CYLINDER

Answer 1

TSA=2πr(r+h)
CSA=2πrh
CSA/TSA=1/3
2πrh/2πr(r+h)=1/3
h/r+h=1/3
3h=r+h
2h=r
CSA=( 1/3)*TSA
2πrh=1/3 of 462
let r be 2h
then,
2*(22/7)*2h*h=154
(44/7)* 2h^2=154
2h^2=154*(7/44)
2h^2=49/2
h^2=49/4
h=√49/√4
h=7/2=3.5cm
r=2h
r= 3.5*2. r= 7cm
volume=πr^2h
= (22/7)*7^2* 3.5
=539cm^3
ans v=539cm^3

Answer 2

given 

T.S.A of cylinder = 462

C.S.A of cylinder = 1/3*462

2πrh = 1/3*462
2πrh = 154                        ..............................1

now,
ATQ,   
        T.S.A of cylider = 462
         2πrh + 2πr² = 462
       154 + 2πr² = 462
           2πr² = 462 - 154
            2πr² = 308
         on solving
        we get , r = 7
       putting value of r in eq. 1 we get,
     h = 77/22
 now ,
 volume of cylinder = πr²h
                               =    22/7 * 7*7 * 77/22
                         on solving we get 
            volume = 539 cubic cm

hope this helps you