Question

Find the area of the surface. 7. The part of the hyperbolic paraboloid z = y2 – x? that lies between the cylinders x + y² = 1 and x² + y² = 4

Answer 1

Solution Page 6 :- Given that the part of hyperbolic parabolwid is Z= y2-2+2 The cylinder equation are 742 + y2 = 1 & It2 + y2 = 4 By using Cylindrical coordinates, O= Coso, y = 9 Sino, ZEZ . t² + y2 = (rcoso)2 + (elsing)2 = 42 (Cos? 0 +51n2o) at² + y2 = 12 dA= er der do Let us find the Radius of the cylinder at² + y2 = 1 & ot² + y2 = 4 12 1 12 = 4 = = 1 t = 2 we know that for cylinder the orange varies from o to 2R. The limits are OLOLZA 120L2 Now ean partialy difft w.rto at & Y. Zat= -221 & Zy=24. : we know that Swrface Anica = SS. 11+ zi +z3.da = 55, ++(-23)2 +(2492 da - Slo 11 + 4x2 + 4y2.ca = SS17+4(124923.com = St V1 +4.312. 31 dor do

Page ① 0 1 = 52"}* 34 5 144.912dando = S3 S2 (1+4912)3/2.dor do = 120 s (1 +442) 3/2 7² do 2 215 = $o 136834 ], 21 = 13" [ (1746393)2 – (14 499% Judo = 5," 17" - 69%] do = (-1972 - 15]*} 546 = $(1143-153)*3 (0)3* = $ { ${1799-169) (21-03 = f ( 3 VT-3759] Surface Area = 2 ( ² 073 -2 153] Ang. Win