高中数学必修二第一章《空间几何体》单元测试卷及答案

PM?PO2?OM2?42?32?5,PN?PO2?ON2?42?42?42.

11V?Sh???8?6??4?64.

33(2)S侧?2S△PAB?2S△PBC?AB?PM?BC?PN?8?5?6?42?40?242.

321.【答案】h2?19h. 3【解析】当锥顶向上时,设圆锥底面半径为r,水的体积为:11?2?219V??r2h???r??h??r2h.

33?3?38121当锥顶向下时,设水面圆半径为r′,则V???r'2?h2.

3?h23r21h22r2h2r又r'?,此时V???2?h2?,

3hh3h2∴

?h23r23h2331921919??rh,∴h2?h. h,即所求h2的值为813322.【答案】(1)AD?36cm;(2)V?50435?cm3

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【解析】(1)设圆台上、下底面半径分别为r、R,AD=x,则OD?72?x, 60????72?R?12?2?R?由题意得?,∴?.即AD应取36cm. 180x?36???72?x?3R(2)∵2?r????OD??36,∴r?6cm, 3322圆台的高h?x2??R?r??362??12?6??635.

11∴V??hR2?Rr?r2???635?122?12?6?62?50435?cm3

33??????

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