Question 1069067
The formula for outside surface area is
{{{ 2*pi*r*h = 2*pi*r*21 }}}
{{{ 2*pi*r*h = 42*pi*r[1] }}}
The inside surface area is:
{{{ 2*pi*r[2]*21 = 42*pi*r[2] }}}
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The difference of the surface areas is equal to
(1) {{{ 42*pi*( r[1] - r[2] ) = 44 }}} cm2
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The volume of the metal is 
[ vol of outside cylinder ] minus [ vol of the hollow part ]
{{{ pi*r[1]^2*21 - pi*r[2]^2*21 = 21*pi*( r[1]^2 - r[2]^2 ) }}}
You are given that:
(2) {{{ 21*pi*( r[1]^2 - r[2]^2 ) = 110 }}} cm3
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(1) {{{ r[1] - r[2] = 44 / ( 42*pi ) }}}
(1) {{{ r[1] - r[2] = .3335 }}}
(1) {{{ r[1] = r[2] + .3335 }}}
and
(2) {{{ r[1]^2 - r[2]^2 = 110 / ( 21*pi ) }}}
(2) {{{  r[1]^2 - r[2]^2 = 1.6673 }}}
(2) {{{  ( r[2] + .3335 )^2 - r[2]^2 = 1.6673 }}}
(2) {{{ r[2]^2 + .667r[2] + .1112 - r[2]^2 = 1.6673 }}}
(2) {{{  .667r[2] + .1112 = 1.6673 }}}
(2) {{{ .667r[2] = 1.5561 }}}
(2) {{{ r[2] = 2.333 }}}
and
(1) {{{ r[1] = r[2] + .3335 }}}
(1) {{{ r[1] = 2.333 + .3335 }}}
(1) {{{ r[1] = 2.6665 }}}
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Outside diameter = 
{{{ 2*r[1] = 2*2.6665 }}}
{{{ 2*r[1] = 5.333 }}} cm
Inside diameter =
{{{ 2*r[2] = 2*2.333 }}}
{{{ 2*r[2] = 4.666 }}} cm
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check answers:
(1) {{{ 42*pi*( r[1] - r[2] ) = 44 }}} 
(1) {{{ 42*pi*( 2.6665 - 2.333 ) = 44 }}} 
(1) {{{ 42*pi*.3335 = 44 }}}
(1) {{{ 131.947*.3335 = 44 }}}
(1) {{{ 44.004 = 44 }}}
close enough
(2) {{{ 21*pi*( r[1]^2 - r[2]^2 ) = 110 }}} 
(2) {{{ 21*pi*( 2.6665^2 - 2.333^2 ) = 110 }}} 
(2) {{{ 21*pi*( 7.1102 - 5.4429 ) = 110 }}} 
(2) {{{ 21*pi*1.6673 = 110 }}}
(2) {{{ 65.9734*1.6673 = 110 }}}
(2) {{{ 109.998 = 110 }}}
close enough