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

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we know that

2(pie)(radius)(height )

height will come 3.5cm

volume= (pie)(radius)square(height)

so volume will come 539 cm cube

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