Question

Find the area of the surface obtained by rotating the circle x^2 +y^2 =3.2^2 about the line y = 3.2. (Keep three decimal places.)

Answer 1

som 6. ret Shift th У 23.? circle x²x₂33-2 В. це ъч 3.2 от +s and Rotate it about saadis will give the same result Now circle х*4 (4-323* = 2.2 -- -- х 10. 24 G. Цч - \о, 24 - x=56.49 z2 Got the right half 3. 2-3 х у (6. – 24) = 1) а) 6. uy-у G.44-у No 4 S - 2 Х2 1+ ( dy 6. 4. цт) у 14 (3.3 - 1 с. ay-уг) У 6. Ц 64 4 +1 ) Ух N6, 49- = 12. қт) 9 dy а) 6.49-52 6, 4 у су 12. Хту з « 3.2 - (9-3-23

Put y 32= 3.2 sint dy=3.2 cost at Now y=3.2 +3-2 sint for uzo, t= -17 9 = 6:4, t = 2 Na => 5=1273 (3:2+3.2 sin t) x 3.2 cost of ✓ (3.2)? (3.2 sint? 12 >> 5725 su 3.2(lt sint) x3.2 costat 3.2 cost -TY2 Tla s-12.8 T x 3.2 (it sint) dt -T/ T/2 40.967 [t-cost] [t-costume {CT (1/₂) (ros Tz COS = 40.967 40.9 GTXT " x 7 = 40.967? 40 4.259 Hence surface are cue = 404.259 Thank you