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M152 Exam2 Au09 Sol

# M152 Exam2 Au09 Sol - r[4r]l Irz Ecfw_4cfw tcfw_L fttl oq...

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1) (u) t{L e shap Irz E{4{ tank in the s maxlmum alr r[4r]l (20 points) A What is the ape unt fttl oq of a.n inverted cone has depth 20 ft and radius 10 ft. of water that the tank can hold? to f{, { = -! 6ealn. I rr(r4'zo f{.3 - ?.ePr ft,! "ft[ (b) How deep is the water in the tank ivhen there are ff ft3 of water in the tank? (--l --ij" WI''V >ohA S'= [,,, a rz" roou.ln' In=,0 t{. (c) How much work is required to pump water out of the tank over the top, wherL thFre are + ft3 o water in the tankl (The density of water 62.5 lb/113.) rtlly : |j (*c a\"o,e) G o\) Av' 'r(f 1\"\j .f\: p , oa, s ,r(irt,i, ir, 64,S"(ll\'(zo- y\ * !-o-! s rr' lq *xtz4 , .h ,.r.z, *.ta ,, v = )6 1rtil) ,x . i l. t-rt 5t'l:= 5h' cto J og'/1gur - .tu',\l'o .i \3, 1,',/lo ' glln 1 .tl.u,.

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2) (20 points) The bas€ oI d solid is the region betwcen the graphs of I : eor and I 5r for 0 :! c<2. Cross sections of the solid that are perpendicular to the ,r axis ale squares. Find the volume o{ the solid. -ir g"*- s ^ ,41^1= S*-s'lt c(, ett) ?l I I (x, Sx) ,-\ ) /r. to" ;1u "16 I |{u..o*d, u't*,! *\$s rh11\ I ox v" \l(ut'-.*\*d" \.("-"- \$*:,*.,. *,i'"1, - [ro-{eq.l]- \$."-,t - [..{e's ,td'-\$-?.''* tr'*J,.]- f -'t: -o -(-i.'-{;)] 5 -!9+ dl t0 -rE 6r
3) (20 points) Fird the following integral lr"o""1sr1a, (Hint: the t g identities on the. attarhed formula sheet may be helpful.)

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