Question

La Tech Stewart8e Ch15Sec7: Problem 6 Previous Problem Problem List Next Problem (1 point) Une cylindrical coordinates to find the volume of the solid that tes within both the cyinder + y - 1 and the sphere 2 + y +

Answer 1

Ans: We have to use cylindrical Coordinates to find the volume of the solid that lies within both the Cylinder x² + y2=1 & the sphere n?ty² +2²=4 Cylindrical Coordinates y=rsino, z=2 x² + y2 =22 g 2 = 1 & 22 +22=4 then 22= 4-02 = 24-22 r=rcoso 2 V= eSSS ir do do dz do do dz Here z from 14-22 to +84-22 r from to 1 to O 27 weef o v= vit zehir rdo do da -54-72 J482 Ikr da} ovde - Jura $422 s ) [ra]. do do 1482 > 2T 12-22 -8 (-5482)] drdo 157 2254-72) drdo 2 'S 27 T(434x2) do} do 21 [ So). S[2x7 2x254-22) do fo 2:14-22. dr 2 = 4T put u=4-82 du = do Now -2x & dr = -1 du Joghoz dr = Xx &. uz du = 1 1 h tu du = -24% = 1u/ 3 ?u=4-82 z (4-22% v = 45 (4-72)3 -49 [ 33 % - (439) 313 - 8] -4X [35 V= ang 32T - 43T 327 V= 33.5238095 - 21.774353 ra 11.7494565 Aug Scanned with CamScanner CS Scanned with CamScanner