Question

Using any method find the volume of the solid between the surfaces z= 8 – y² and z = 22 + y2

Answer 1

Clue and Given circular parabolaid eportion z = 8-2-2 this Sulia Pruded z = 2 + 4 Dej aduan pemakat? again x² + y 222 +2y = 8 => x² + y = 8 = 4 2 So 용의 추 2 vabime, 16,2) îty²=4 20) (210) nemist 6-2007 2=2-17 [0,-2) S volume of solid Iffar And again Because of the two circle we will coordinates the intersection pagrabola is a using cylintrical

where dy is dv is equal to releder.de Im cylindrical.coorralimate volume obedy dz= rardada So ve fff or forte de la And limit fowen Jimit of equation z=2²ty? . ² and then upper limit of equation 2 8-82 8- (pity?) 852 The limit for 2= 8_ and limit of or and will use the intersection of the two paraboloids projected on to the xy plan which is this circle here. The limits of integration for r from zero to #2 The limits of integration for a going be care

around the circle colo which is from -22010 ardz drdo 27 8-82 Ilean da do 27 8.92 Oz dardo 22 2 ra Tor (8-82) - 83 dodo -23 23] dor do . 2 27 [ 8r - 283] do do 2 234 doo 2x 22 goric 8 do 1x 16 do 6 27 (se) 168 unit cube