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3. 王先生准备购买一辆轿车，到4S店询价，得知：如果分期付款的话，一共付的钱要比目前定价多付10%，如果现在用现金一次性付款的话，能打九五折，两种付款方式有30000元的差价。这辆轿车目前的定价是多少万元？（4分）
答案
3.$30000÷(1+10\%-95\%)=200000$（元）$=20$（万元） 答：略
解析
【分析】首先将轿车目前的定价看作单位“1”，分别确定分期付款和现金一次性付款对应的定价分率，两种付款方式的差价30000元对应两者分率的差值，用差价除以该分率差值即可求出单位“1”（即轿车定价），最后换算单位得到结果。
【解析】把轿车目前的定价看作单位“1”：
1. 分期付款的钱占定价的分率：$1 + 10\% = 110\%$
2. 现金一次性付款的钱占定价的分率：$95\%$
3. 差价对应的分率：$110\% - 95\% = 15\%$
4. 轿车定价：$30000 ÷ 15\% = 200000$（元）$= 20$（万元）
【答案】20万元
【知识点】百分数的应用、单位“1”的确定
【点评】本题为基础百分数应用题，关键是找准单位“1”及差价对应的分率，通过除法计算单位“1”的量，解题思路清晰，难度适中。
【难度系数】0.6
【解析】把轿车目前的定价看作单位“1”：
1. 分期付款的钱占定价的分率：$1 + 10\% = 110\%$
2. 现金一次性付款的钱占定价的分率：$95\%$
3. 差价对应的分率：$110\% - 95\% = 15\%$
4. 轿车定价：$30000 ÷ 15\% = 200000$（元）$= 20$（万元）
【答案】20万元
【知识点】百分数的应用、单位“1”的确定
【点评】本题为基础百分数应用题，关键是找准单位“1”及差价对应的分率，通过除法计算单位“1”的量，解题思路清晰，难度适中。
【难度系数】0.6
4. 甲、乙两辆汽车分别从A、B两地同时出发，沿同一条公路相向而行，两车在距离中点15 km处相遇，甲车与乙车的速度比是6∶5，求A、B两地的距离。
（4分）
（4分）
答案
4.$15÷(\frac{1}{2}-\frac{5}{11})=330$（km） 答：略
解析
$＜[bou_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD54_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD77_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SILENT_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[/audio_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[UNK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD67_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD95_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[botu_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/hiddenthink＞＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞$$＜[SOG_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD86_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD77_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD92_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD78_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|FCResponseBegin|$＞＜parameter_never_used_51bce0c785ca2f68081bfa7d91973934=＜[EOG_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD75_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SEP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SOI_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD89_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SEP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD81_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD90_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD82_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD62_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaCreation＞＜[PLHD65_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD82_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SPEAK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD77_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜/doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD58_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD89_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD95_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD60_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD85_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD69_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD100_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD91_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD60_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD68_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD55_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/think_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD76_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/think_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[SEP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD64_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD67_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaShow＞＜[SOGP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD80_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD65_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/think_never_used_51bce0c785ca2f68081bfa7d91973934＞$ $＜[PLHD82_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PAD_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜function_never_used_51bce0c785ca2f68081bfa7d91973934=＜RichMediaShow＞＜RichMediaShow＞＜doubao_withdraw＞＜[PLHD68_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SOGP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|FCResponseEnd|$＞＜[PLHD80_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[botu_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD81_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD77_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD100_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD85_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD74_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD69_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaReference＞＜[PLHD76_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/function_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaReference＞＜[PLHD71_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[UNK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[eou_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[eotu_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[botu_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD77_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[EOG_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD67_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜parameter_never_used_51bce0c785ca2f68081bfa7d91973934=＜[SILENT_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD94_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜parameter_never_used_51bce0c785ca2f68081bfa7d91973934=＜/RichMediaShow＞＜[PLHD68_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[CLS_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD60_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|video|$＞:＜[PLHD76_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[CLS_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD56_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|FCResponseBegin|$＞＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD66_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD97_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD89_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD85_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD57_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD84_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD55_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD87_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SOI_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD99_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|image|$＞:＜[PLHD88_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜parameter_never_used_51bce0c785ca2f68081bfa7d91973934=＜[PLHD86_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜parameter_never_used_51bce0c785ca2f68081bfa7d91973934=＜[PLHD73_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD72_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD93_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|FCResponseEnd|$＞＜[PLHD56_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|paragraph|$＞:＜[PLHD64_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD78_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SOGP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|paragraph|＞:＜|FCResponseBegin|＞$＜[PLHD73_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD69_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD87_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaCreation＞＜[bou_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaCreation＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜$|superscript|$＞:＜RichMediaShow＞＜[PLHD72_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/escapeShell＞＜[PLHD82_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜hiddenthink＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD99_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD66_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD91_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[bou_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD97_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD83_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD98_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD74_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaShow＞＜[UNK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaReference＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD89_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜RichMediaReference＞＜[PLHD97_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD77_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaCreation＞＜function_never_used_51bce0c785ca2f68081bfa7d91973934=＜[PLHD95_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD94_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜parameter_never_used_51bce0c785ca2f68081bfa7d91973934=＜[PLHD87_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD87_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/parameter_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD68_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[MASK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD54_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD68_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SOG_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaCreation＞＜[PLHD84_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/escapeShell＞＜$|card|＞:＜|FCResponseBegin|$＞＜[PLHD97_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD84_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD90_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[EOI_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[eou_never_used_51bce0c785ca2f68081bfa7d91973934]＞$ $＜[PLHD82_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[bou_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD94_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD61_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD84_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|card|$＞:＜[PLHD73_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD72_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|video|$＞:＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD83_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD88_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[eou_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD69_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PAD_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD62_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/think_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[CLS_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜doubao_withdraw＞＜[PLHD66_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD89_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD86_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD95_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜/hiddenthink＞＜[MASK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD75_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD62_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|superscript|$＞:＜/RichMediaReference＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaReference＞＜[SOG_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[MASK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD82_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD100_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD100_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD82_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaReference＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD93_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD54_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SILENT_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD72_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaShow＞＜[PLHD89_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD55_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaShow＞＜[PLHD90_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaReference＞＜[SEP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD62_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD86_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[BOS_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD89_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[MASK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaReference＞＜$|video|$＞:＜[PLHD85_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD86_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD80_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD60_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD82_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[bou_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD97_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD99_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/parameter_never_used_51bce0c785ca2f68081bfa7d91973934＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[/audio_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD71_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD94_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD80_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD68_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD100_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD70_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD56_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD81_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD64_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜$|FCResponseEnd|$＞＜[PLHD90_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD81_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|FCResponseBegin|$＞＜function_never_used_51bce0c785ca2f68081bfa7d91973934=＜/hiddenthink＞＜[PLHD64_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|superscript|$＞:＜[PLHD61_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD74_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/escapeShell＞＜/think_never_used_51bce0c785ca2f68081bfa7d91973934＞＜$|FCResponseEnd|$＞＜[PLHD94_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD64_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[botu_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|superscript|$＞:＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜$|superscript|$＞:＜[PLHD43_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaShow＞＜[PLHD69_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD91_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD84_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[EOI_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD82_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|superscript|$＞:＜[PLHD67_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD86_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜$|FCResponseEnd|$＞＜[PLHD94_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD76_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜/escapeShell＞＜[PLHD76_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD81_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD76_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜escapeShell ＜[PLHD88_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD71_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD83_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[CLS_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[eotu_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD87_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaShow＞$$＜/RichMediaCreation＞＜doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD76_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD99_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD63_never_used_51bce0c785ca2f68081bfa7d91973934]＞$$＜[PLHD72_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaReference＞＜parameter_never_used_51bce0c785ca2f68081bfa7d91973934=＜$|superscript|$＞:＜/hiddenthink＞＜/parameter_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[audio_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD77_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD98_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD100_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜RichMediaCreation＞＜[PLHD97_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD97_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/hiddenthink＞＜[PLHD94_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD65_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/function_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD75_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SPEAK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|card|$＞:＜[PLHD71_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD91_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD77_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[UNK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD57_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜$|FCResponseEnd|$＞＜[PLHD79_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD71_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD81_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/function_never_used_51bce0c785ca2f68081bfa7d91973934＞$
5. 赵师傅向如下左图所示的空容器（由上、下两个圆柱组成）中均匀注油，正好注满。注油过程中，容器中油的高度与所用时间的关系如下右图所示。
（1）把下面的大圆柱注满需要（
（2）上面的小圆柱高（
（3）如果下面的大圆柱的底面积是$48\ \mathrm{cm}^2$，那么大圆柱的体积是多少立方厘米？上面小圆柱的底面积是多少平方厘米？（写出计算过程）（2分）
（1）把下面的大圆柱注满需要（
$\frac{4}{3}$
）分钟。（2分）（2）上面的小圆柱高（
30
）cm。（2分）（3）如果下面的大圆柱的底面积是$48\ \mathrm{cm}^2$，那么大圆柱的体积是多少立方厘米？上面小圆柱的底面积是多少平方厘米？（写出计算过程）（2分）
答案
5.(1)$\frac{4}{3}$ (2)30
(3) 大圆柱的体积：$48×20=960$（$\mathrm{cm}^3$）
$(2-\frac{4}{3})÷\frac{4}{3}=\frac{1}{2}$ $960×\frac{1}{2}÷30=16$（$\mathrm{cm}^2$） 答：略
(3) 大圆柱的体积：$48×20=960$（$\mathrm{cm}^3$）
$(2-\frac{4}{3})÷\frac{4}{3}=\frac{1}{2}$ $960×\frac{1}{2}÷30=16$（$\mathrm{cm}^2$） 答：略
解析
【分析】
首先观察油的高度与时间的关系图：注油过程分为两个阶段，第一阶段注入下方大圆柱，油的高度上升较慢（图像斜率小），对应注满大圆柱的过程；第二阶段注入上方小圆柱，油的高度上升变快（图像斜率大），对应注满小圆柱的过程。解题时需分段提取图像信息，结合圆柱体积公式和均匀注油时单位时间注油体积不变的特点，逐步求解各问题。
【解析】
（1）从图像可知，油高上升较慢的阶段结束时（油高20cm，即大圆柱的高度），对应的时间为$\frac{4}{3}$分钟，因此注满大圆柱需要$\frac{4}{3}$分钟。
（2）注满大圆柱后，油继续上升至总高度50cm时注满容器，所以小圆柱的高度为$50 - 20 = 30$cm。
（3）①大圆柱体积：根据圆柱体积公式$V=S×h$，大圆柱体积为$48×20=960$（$\mathrm{cm}^3$）；
②均匀注油时单位时间注油体积不变，注油速度为$960÷\frac{4}{3}=720$（$\mathrm{cm}^3/$分钟）；
③注小圆柱的时间为$2-\frac{4}{3}=\frac{2}{3}$分钟，小圆柱体积为$720×\frac{2}{3}=480$（$\mathrm{cm}^3$）；
④小圆柱底面积：$480÷30=16$（$\mathrm{cm}^2$）。
【答案】
（1）$\frac{4}{3}$；（2）30；（3）大圆柱体积是960$\mathrm{cm}^3$，小圆柱底面积是16$\mathrm{cm}^2$。
【知识点】
圆柱体积、函数图像应用
【点评】
本题结合圆柱体积与函数图像，考查分段分析问题的能力，核心是区分注满上下圆柱的阶段，利用均匀注油的体积不变性解题，是中等难度的综合应用题。
【难度系数】
0.5
首先观察油的高度与时间的关系图：注油过程分为两个阶段，第一阶段注入下方大圆柱，油的高度上升较慢（图像斜率小），对应注满大圆柱的过程；第二阶段注入上方小圆柱，油的高度上升变快（图像斜率大），对应注满小圆柱的过程。解题时需分段提取图像信息，结合圆柱体积公式和均匀注油时单位时间注油体积不变的特点，逐步求解各问题。
【解析】
（1）从图像可知，油高上升较慢的阶段结束时（油高20cm，即大圆柱的高度），对应的时间为$\frac{4}{3}$分钟，因此注满大圆柱需要$\frac{4}{3}$分钟。
（2）注满大圆柱后，油继续上升至总高度50cm时注满容器，所以小圆柱的高度为$50 - 20 = 30$cm。
（3）①大圆柱体积：根据圆柱体积公式$V=S×h$，大圆柱体积为$48×20=960$（$\mathrm{cm}^3$）；
②均匀注油时单位时间注油体积不变，注油速度为$960÷\frac{4}{3}=720$（$\mathrm{cm}^3/$分钟）；
③注小圆柱的时间为$2-\frac{4}{3}=\frac{2}{3}$分钟，小圆柱体积为$720×\frac{2}{3}=480$（$\mathrm{cm}^3$）；
④小圆柱底面积：$480÷30=16$（$\mathrm{cm}^2$）。
【答案】
（1）$\frac{4}{3}$；（2）30；（3）大圆柱体积是960$\mathrm{cm}^3$，小圆柱底面积是16$\mathrm{cm}^2$。
【知识点】
圆柱体积、函数图像应用
【点评】
本题结合圆柱体积与函数图像，考查分段分析问题的能力，核心是区分注满上下圆柱的阶段，利用均匀注油的体积不变性解题，是中等难度的综合应用题。
【难度系数】
0.5
