Evaluate the triple integral AP 2 over the solid region E enclosed by the two surfaces z= 4/z² + y? and = z² + } .
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- Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a lateral area. b total area. c volume.For the sphers x-12+y+22+z-42=36 and x2+y2+z2=64, find the ratio of their a surface areas. b volumes.Determine the surface area of the solid obtained by rotating y=/9-x from -2sxS2 about the x -axis.
- Determine the volume of the rotating object that occurs if the area of the curve y1 = - x2 + 4 and the line y2 = - 2x + 4 , is rotated around the x axis, a distance of 360°?. Make the boundaries of the curve area!Determine the area of the surface generated by y=x^3 on [0,1], about the x-axis. Final Answer is A(s)=3.563 sq. units, Show the complete solution.1/ Find the area of the region enclosed between the curves y= 2x²+10 and y=4x+16 and ,x=-2 and x-5? ans/ 142/3 2/ determine the area of the region enclosed between the curves x=y2-3 and y=x-1? ans/ 18 3/ Find the area of the region enclosed between the curves y= x³ and x= y ? ans/ 1/2 4/ Find the area of the region enclosed between the curves y= cos 2x, y=0, x=TT/4, x= TT/2 ? ans/ 1/2 5/ Find the volume of the solid generated by revolving the area enclosed by y= x², y=0, x=1 about 1) y-axis 2) x=1 3)y=1 ans/ 1) v=TT/2 2) v= TT/6 3) 7TT/ 15 6/ use cylindrical shell to find the volume of the solid generated when the region under 2y=x+4, y=x, x=0 is revolving about 1)y- axis ans/ 1) 32 TT/3 2) x-4? 2) 64 TT/3
- Find a center of mass of a thin plate of density 8 = 6 bounded by the lines y = x and x = 0 and the parabola y = 2-x² in the first quadrant. x=y= (Type simplified fractions.)THE AREA BETWEEN THE CURVES 2 4 y = x² AND y² = 4X IS REVOLED ABOUT THE LINE X = -1. SOLVE FOR THE SOLID OF REVOLUTIONThe net of a rectangular prism and its dimensions äre shoWH II 10.5 cm 10.S cm S CIm 8 cm 12 cm 12 Cm What is the total surface area of the rectangular prism in square centimeters? (7.90, 5S, RCI} F 612 cm' G 2,016 cm' H 306 cm' J 1,008 cm of the