現(xiàn)有亂成一團(tuán)的鐵絲和銅絲各一捆(可以稱(chēng)出每捆質(zhì)量).已知鐵絲和銅絲的截面半徑分別為r1cm和r2cm,請(qǐng)你設(shè)計(jì)一種方案,不用直接測(cè)量長(zhǎng)度,就能計(jì)算這捆鐵絲和這捆銅絲的長(zhǎng)度差(注:鐵的密度約為8g/cm3.銅的密度約為9g/cm3).
解:設(shè)一捆鐵絲和銅絲的質(zhì)量分別為m
1g,m
2g,則這捆鐵絲的長(zhǎng)=
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,這捆銅絲的長(zhǎng)=
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,
所以這捆鐵絲和這捆銅絲的長(zhǎng)度差=
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-
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=
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.
分析:設(shè)一捆鐵絲和銅絲的質(zhì)量分別為m
1g,m
2g,根據(jù)密度公式得到這捆鐵絲的長(zhǎng)=
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,這捆銅絲的長(zhǎng)=
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,然后求它們的差.
點(diǎn)評(píng):本題考查了分式的混合運(yùn)算:分式的混合運(yùn)算,要注意運(yùn)算順序,式與數(shù)有相同的混合運(yùn)算順序;先乘方,再乘除,然后加減,有括號(hào)的先算括號(hào)里面的.