正六棱锥P-ABCDEF中,G为PB的中点,则三棱锥D-GAC与三棱锥P-GAC体积之比为________.
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2:1
解析分析:由于G是PB的中点,故三棱锥P-GAC的体积等于三棱锥B-GAC的体积;求出DH=2BH,即可求出三棱锥D-GAC与三棱锥P-GAC体积之比.
解答:解:由于G是PB的中点,故P-GAC的体积等于B-GAC的体积在底面正六边形ABCDER中BH=ABtan30°=AB而BD=AB故DH=2BH于是VD-GAC=2VB-GAC=2VP-GAC则三棱锥D-GAC与三棱锥P-GAC体积之比为 2:1故