Question 1098758
Let {{{ A[1] }}} = the area of the 
base of the 12 cm tall bucket in cm3
Let {{{ A[2] }}} = the area of the
base of the 18 cm tall bucket in cm3
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{{{ 12/A[1] = 18/ A[2] }}}
{{{ A[2]*18 = 168.75 }}} 
{{{ A[2] = 9.375 }}} cm2
{{{ 12/A[1] = 18/9.375 }}}
{{{ 12/A[1] = 1.92 }}}
{{{ 1.92A[1] = 12 }}}
{{{ A[1] = 6.25 }}} cm2
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{{{ V]1] = A[1]*12 }}}
{{{ V[1] = 6.25*12 }}}
{{{ V[1] = 75 }}} cm3
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The volume of the smaller bucket is 75 cm3
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check:
{{{ 12/A[1] = 18/A[2] }}}
{{{ 12/6.25 = 18/9.375 }}}
{{{ 12*9.375 = 18*6.25 }}}
{{{ 112.5 = 112.5 }}}
OK