Question

A solid cylinder has tsa 462cmsquaee it's csa is 1/3 of its tsa find the volume of the cylinder

Answer 1

after that
we know that
2(pie)(radius)(height )
height will come 3.5cm
volume= (pie)(radius)square(height)
so volume will come 539 cm cube

Answer 2

TSA = 2 * 22/7 * r (h+r) = 462 cm square
CSA = 2 * 22/7 *r*h  = 1/3 of TSA
                                 = 1/3 x 462 = 154      ____ 1

   TSA = 2 * 22/7 * r (h+r)
           =  2*22/7 * r*h  + 2*22/7 * r*r
   462       = 154 + 2*22/7*r*r
2*22/7*r*r = 462 - 154 =308
r*r = 308 * 1/2 * 7/22 = 49
                 ( r = 7)      ___________________2
sub r=7 in 1st equ.
2* 22/7 * r* h = 154
on solving (h = 7 /2)
Volume of Cylinder = 22/7 * r* r* h
                               = 22/7 * 7*7*7/2 = 529 cm cube