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SolidsDisks - The base of the solid is the Cirele 3:2 113 1...

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Unformatted text preview: The base of the solid is the Cirele 3:2 +113 : 1. Cross sections are perpendicular to the x—axis are. semi-circular disks with diameters in the xy—plane. The base of the. solid is the Circle .32 + y2 = 1. Cross sections are perpendicular to the x—axis are squares with bases in the xy—plane. The base of the solid is the circle :172 +112 2 1. Cross sections are perpendicular to the x—axis are equilateral triangles with bases in the xy—plane. The volume of the solid with base {(x,y):y S :1: _<_ 4}. Cross sections are perpen lcu ar to the x-axis and are semi—circular disks. The region between the curve y : fl 0 S .1: g 4, and the x—axis is revolved around the x—axis to generate a solid. Find its volume. Find the volume of the solid generated by revolving the region between the y axis and the curve :1: : 1 S y S 4 about the y—axis. Q |l¢ Rotating about lines that aren’t the axes Find the volume of the solid generated by revolving the region between the parabole :1? : y:l + l, and the line x=3 about the line x=3. _\- Rm -— 3 _(_\~1 + I) («35% = l — \2 \l) ' _\\ (3.63:) ') ,\' (a) Solids with holes in them! The region enclosed by the curves y = .1: and y : .I:2 is rotated about the x—axis. Find the volume of the result.ng solid. The region bounded by the parabola. y = 3:2 and the line y ; 2.1: in [he first quadrant. is revolved about the y—axis to generate a. solid. Find the volume of the solid. InIL'nul of imcgrnlion Rotating things with holes about things other than the axes Find the volume of the solid obtained by rotating the region bounded by y = 132 and y = a? about, the line y = ‘2. ' w . Find the volume of the solid obtained by rotating the region. bounded by y = $2 and y : .1: about the line j 4-" !+\.r'l'\' -—'<- — -’ I I I «Axn- ——’1 :- I. 1 l .._ filfl __.} ; :1,- : —1. ...
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