Use polar coordinates to find the volume of the solid that is above the
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- Use polar coordinates to find the volume of the solid above the xy-plane, under the plane y + z = 4 and within the (x - 1)² + y² = 4.arrow_forwardFind the coordinates of the centroid of the region bounded by y=10x² and y=2x³. The region is covered by a thin, flat plate. Find the coordinates of the centroid of the solid generated by revolving the region bounded by y=7-x, x=0, and y=0 about the y-axis. Assume the region is covered by a thin, flat plate. The coordinates of the centroid are (Type an ordered pair.) The coordinates of the centroid are (Type an ordered pair. Round each coordinate to two decimal places as needed.) ECCO d=cm (Round to one decimal place as needed.) Find the center of mass (in cm) of the particles with the given masses located at the given points on the x-axis. 36 g at (-3.7,0), 29 g at (0,0), 21 g at (2.2,0), 80 g at (2.9,0)arrow_forwardFind the volume of the solid by subtracting two volumes. the solid enclosed by the parabolic cylinders y = 1 - x², y = x² - 1 and the planes x + y + z = 2, 3x + 6y -z + 15 = 0arrow_forward
- Using polar coordinates, evaluate the volume of the solid in the first octant bounded by thehemisphere (Handwritten please)arrow_forwardFind the volume of the solid under the surface z = 3x + 5y2 and above the region in the first quadrant bounded by y = x³ and y = 4x. Use polar coordinates to find the volume of the solid that is bounded by the paraboloids z = 16-r² - y², z = x² + y² - 16. Use polar coordinates to find the volume of the solid that is bounded by the plane z = 0 and the cone z = 3-√√√x² + y². . Find the area enclosed by r = cos(30) and the cardioid r = 1 + cos(0). pu mi 1. Fin 2. Fin 3. Con 4. Comarrow_forward(b) Find the volume and the surface area of the truncated cone made by the rotation of the solid line around the x axis as shown in the figure. y 4 3. -4 -3 -2 -1 3. 4. -3 -4arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,