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設圓錐的底面半徑為r,母線為l,則2πr=13πl,得l=6r,S=πr2+πr•6r=7πr2=15π,得r=157,圓錐的高h =l2-r2=35r即h=35•157,V=13πr2h=13π×157×35×157=2537π.故答案為:2537π.
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