catto - math.ucla.edujhrooney/W18/content/feb01.pdf · Discussion 4 bndinahytmsandapphiahnr...
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Discussion 4 bndinahytmsandapphiahnr February 1,2018 1 Describe the following wnhutiwmhiutowfaus : ¥mht x=rwnl Cglindninl coordinated Cspheimlwudmihst ( III. (a) r=ro (d) p=po aphid (b) 0=00 (e) 0=00 x=psm¢wsO catto a # % &IgwmYfm° (a) cylinder (d) sphere (b) half . plane (e) half . plane (c) higutnlpbme (f) cone @ Find quutmsinyhmilwndinuhrfntheplanetzocamhmlt and thophueofmdiusasoantdatlo ,0,a) . Futheplane , zo=z=pws¢ . Fnttuphm , p=2aws¢ . @ Findttuamugevaheoffex .gr#yrauttudihD=fk.peR4x2tyIaT . Thanafttudishisnei, wthanuyevuhuis t.at#updA=tTazfYToayrrdaradI=aFfoar2dr=I2I . fthusthewuageditunufmapintinthedihtotheoigiismnethmhlfthemdins . ]
Transcript of catto - math.ucla.edujhrooney/W18/content/feb01.pdf · Discussion 4 bndinahytmsandapphiahnr...
Discussion 4bndinahytmsandapphiahnr
February 1,2018
�1� Describe the following wnhutiwmhiutowfaus:
¥mhtx=rwnl
Cglindninlcoordinated Cspheimlwudmihst ( III.
(a) r=ro (d) p=po
aphid
(b) 0=00 (e) 0=00x=psm¢wsOcatto
a # %&IgwmYfm°
(a) cylinder (d) sphere
(b) half . plane (e) half .
plane
(c) higutnlpbme(f) cone
@ Find quutmsinyhmilwndinuhrfntheplanetzocamhmlt and
thophueofmdiusasoantdatlo,0,a) .
Futheplane, zo=z=pws¢ . Fnttuphm, p=2aws¢ .
@ Findttuamugevaheoffex.gr#yrauttudihD=fk.peR4x2tyIaT.
Thanafttudishisnei, wthanuyevuhuis
t.at#updA=tTazfYToayrrdaradI=aFfoar2dr=I2I .
fthusthewuageditunufmapintinthedihtotheoigiismnethmhlfthemdins.]
�4� hlwhte the volume of the"
in cream one
"
bounded
bebwhyzFxEjanlabwebyx7y7zt4.vohme-fMfFYo2p3m4dpd4dO-2itCfFsmodDHo2pdp-lantkHsh-ybgIrdTfthwmwheanirthisisinyhimalamdinahoD@LetRbettunlidbullofnadinsaantudatGoid.bmputoHsEdV.fffsEdV-fYfFfomwkCprwiedfismAdpd01dO.net
V
= 2*fo¥fowHp4ws4sm¢dpd¢
= 64yd fo÷ wsttsiitdp
=¥t€
�6� Let
Rbetteregwnboumhdobwebyttepamboloidz-6-xtjandbehwbytheunez-xFy.hmptufffzzdV.Usinyglindnidwordinethgthemfmsaez-G-r2andz-r.whikinluntwhmr-z-6-r2-sr-2.Thns.fffeav-fohtfoYrtr2zrdIrd0dV-2nfohfrttzrdzdr-nfo2fltFFrifrdr-iTfo2lrEl3r3t36ddr-ftti@hmputettuameyetitmnfumajomtinttuwlidballB-kxiy.zIeR3Ix2ty7EeaYtottubounduyofB.welldothisinphinwlwoulinaty.lfapintqinBhusrphniulwoulinahslpl9d.thmpisthedintmefumttooigintoq.wapisttuditamfumqtothebmdeyofB.Theballhasvohme5tita3wtkaumgevaheisEaEEfoaCa-plp3mAdpd0doe3zHotsm4ddHoalaffldpHFTTT-as.gd.g
÷
@ Find the untnfmamfaanifumnlid hemisphere A of radius a .
We can ammelhetttw hemisphere Issitting onttuxy . planeand centered
on the taxis . By symmetry , ×=j=o ,and
⇐ k¥Ns
Sz DV
= I ME to lpw . Afismcddpdodo
=
at (fo÷ws¢m¢d¢) ( [ pdp)⇒ 4
= £72 T
@ Fmdttnwlumefaballofmdinsauntelatloialbyinhgatginyhniwlwndinaho .
r.¥€??"
that
.es?so.pnxqatdo=2nfF2fow*psin4dpd4u=wsp=lbnF/Psm4ws34dydu=-sm$d0=tbjtIfIu3dn=#Ta
