∵AB=BC=1,〈ABC=90度,
∴△ABC是RT△,
AC=√2,
∵是直三棱柱,
∴AD⊥平面ABC,〈DAC=90度,
∴〈DCA就是CD与平面ABC所成角,
〈DCA=45度,
∴△DAC是等腰RT△,
AD=AC=√2,
S△ABC=AB*BC/2=1/2,
∴VD-ABC=（S△ABC）*AD/3
=（1/2）*√2/3=√2/6.