設(shè)圓錐的底面半徑為r,高為h,母線(xiàn)長(zhǎng)l,則h=√(l²-r²)
依題意得S=πr²+πrl=πa²,得l=(a²-r²)/r,故
V=(1/3)πr²h
=(1/3)πr²√(l²-r²)
=(1/3)πr²√[(a²-r²)²/r²-r²]
=(aπ/3)r√(a²-2r²)
=(aπ/3√2)√2r√(a²-2r²)
≤(aπ√2/6)[2r²+(a²-2r²)]/2
=πa³√2/12(當(dāng)且僅當(dāng)2r²=a²-2r²,即r=a/2時(shí),“=”取到)
zxqsyr 21:02:59