Question 588032
{{{ V=b^3-6b^2+9b }}}
Factor out {{{b}}}
{{{ V = b*( b^2 - 6b + 9 )  }}}
{{{ V = b*( b - 3 )^2  }}}
{{{ b }}} is the height and
{{{ b - 3 }}} is the side of the square bottom
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given:
{{{ b = 18 }}} in
{{{ b - 3 = 15 }}} in
{{{ V = 18*15^2 }}}
{{{ V = 4050 }}} in3
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{{{ V = 20000 }}} in3
Here's the graph:
{{{ graph( 500, 400, -10, 50, -1000, 25000, x^3 - 6x^2 + 9x ) }}}
It looks like {{{ b = 29 }}} That would be
{{{ V = 29*26^2 }}}
{{{ V = 19604 }}} close
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