Question

Find the volume of the solid obtained by rotating the region A in the figure below about the line x = 5. 20607 3 x y y = x + 2 А 2 B х 5

Answer 1

Ans 27 outerra dins y=2(?+2 dy tema innu 2 radius Atx=5 y=52+2 2572 27 - Solid of reuoluhon 5 x = 5 outerradius b Outer radius = 5 (distance of x=5 from yaxis ) inner radius 5-3 (x coordinate of curve substracted from) E 5- Vy-2 : y=x²+2 3) x = Vy-2 But for given region 270 6. Vy-2 Now by disc method volume => " (ou to come and I dy a = 2 (lower limit ofy) 6=27 (upperlimit ofy) JT (5 (5-vy-2)})dy =fr (25 - (25+4-2-108y-2) dy = 57(265-85 -9 +2 +lo Vy-2) dy = Sto (2-yt 10 vy-2) dy Substitute let 3-2 et =) dy =dt [=2 t = 2-2=0 =dt (y=2 t = 2-2=0, y = 27 t =27-2=25] TI / Ettore dat E" [-x+3tºn)" = 1 (425)* +246)*] (625 a11636,24617 27 27 2 2 2 27 27 2 2 25 0 Q TT 250] -1312511