Question

2: Consider the curve with equation x2/3 + y2/3 = 1. -0.5 0 -0.51 a: Find the exact length of the curve. (Make good use of the symmetric property of the graph. ) b: Find the surface area of the solid obtained by rotating the curve about y-axis. (Watch out for the symmetric property of the graph.)

Answer 1

Solution Given equation of 2213 +423 Parametric equation: . x= cogbo, y= sihzan 040527 a = 360sto sino, y'= 3 smo coso, - No { Because of the then symmetry) - 0=0 then length = Afte?+ 14, 2]" do a fost scoglasikiongeanta con lojte - le ju she came [ Cayle tsiklo gados 60 . Siholosco 050 - = 12 Al2 sino caso de 462 - Let sinco= t = cosado=dt then 212. f tdk=12 (52 0 [sub230) 2 | length = o[1-0] = 6 Ans. Surface Area about y-axis is A for petron foto tyly2 doo es salted of Because of the Symmetry) IM2

May 14.) 2 do 6 - =2120 f colof glo. We shotg sihto lose?o) do = 2x2T A = 2x2a $ 3.2010 She-coco (Coso+56?0) 2de A = 2 x64 s cesto siko do sinotalo=1 ozo Cayot then Let sino do=-dt A =26* f ** (-4) = -LIST A-_-576xf 604501 -- MALI 0-1] with = obed (2) 3 135 hod.. css