(本小題滿分14分)
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如圖,在四棱錐
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中,底面
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是正方形,側(cè)棱
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底面
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,
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,
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是
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的中點。
(1)證明:
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;
(2)求
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以
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為軸旋轉(zhuǎn)所圍成的幾何體體積。
(2)
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解:(1)連接
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交
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于
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,連接

…………2分
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
是正方形,
∴
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為
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中點,
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為
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的中點,
∴
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…………………5分
又
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平面
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,
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
………………7分
(2)過
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作
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的垂線,垂足為
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,
則幾何體為
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為半徑,分別以
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為高的兩個圓錐的組合體
側(cè)棱
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底面
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∴
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,
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,
∴
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……………………9分
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…………10分
=
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…………12分
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=
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…………14分
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