Find the volume and centroid generated by revolving the given plane area about the indicated axis in the picture. Graph.

Q: 21. Rj about AB

A: Changing the coordinates axis so that y axis coincides with AB. The equation of OB becomes:  x=y-1,…

Q: Determine the larger volume. Assume there is a hemisphere which has a radius of 5cm was cut by a…

A: A sphere of radius 5. V = Volume of hemi-sphereV = ∫02π∫0π2∫05r2sinθdrdθdϕ r : radial distance from…

Q: y? = 4x, y = 2x - 4; about y-axis

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Find the Volume of the solid generated by revolving the region of (the figure below) about the line…

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Q: Find the volume of the region in the first octant cut from the solid sphere ps 6 by the half-planes…

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Q: Find the area of the region bounded by the given curves and find the volume of the solid formed when…

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Q: Determine the volume generated by revolving the plane figures about y axis. 4m 3m 1m 2m 4m 2m

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Q: Find the volume when the following region is rotated about the y-axis: y = √4x², y = 0, x = 0.

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Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: According to the given information, it is required to calculate the volume of the solid generated by…

Q: Use polar coordinates to find the volume of the given solid. Under the cone. := V² + y² And above…

A: Consider the provided information, z=x2+y2 and above the disk x2+y2≤9. Use the polar coordinate to…

Q: Use polar coordinates to find the volume of the given solid.

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Q: Find the volumes of the solids obtained by rotating the region bounded by the following curves about…

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Q: Find the volume of a stereoscopic body by rotating a given straight line around an axis surrounded…

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: Find the volume and centroid generated by revolving the given plane area about the indicated axis:

A: Given:  fx = y = x2gx= y = 4x-x2For finding point of intersection, Put fx = gx.…

Q: Find the volume of the solid obtained by rotating about

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Q: Find the volume cm^3 of the solid figure in Fig 1182 that was generated by rotating the shaded…

A: Volume of revolution

Q: Find the volume of the region enclosed by the paraboloid (x-1)²+y? =z and the plane 2x+z=2.

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Q: 4. y= 6x- x', y = x? - 2x, y = -1

A: We find the volume.

Q: Use the Shell method to find the given volume of rotation. A sphere of radius r

A: We take an upper half of a circle of radius r and then rotate it about the x-axis. Equation of the…

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: Given data:     The given function is: y=2(x)1/4. The given limits of y is: [a,b]=[0,2].   The given…

Q: Use the Theorem of Pappus to find the volume of the given solid. The solid obtained by rotating the…

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Q: 7. Find the volume and centroid generated by revolving the given plane area about y^2=4x, x=4; about…

A: Given that - y2 = 4x, x = 4; about x = 4

Q: Find the volume of the Solid by rotating the region. A in the figure about X=-T6 Y=x3+b b. B a…

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Q: Determine the volume generated by revolving the plane figures about line a-a. a y 3m 2m 2m 2m 2m 2m…

A: ----------------------------------------------------------------------------- Equation of line…

Q: 4. y= 6x -x², y = x² – 2x , y = -1

A: Given that     y = 6x-x2 , y=x2-2x , y=-1 Here we have to find the volume and the centroid.

Q: find the volume of the solid obtained by rotating region B in Figure 13 about the givenaxis. y = 6

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Q: use the disk method to find the volume (in units^3) when the regionbounded by the curves x+y=5, x=0,…

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Q: Find the volume of the solid formed by rotating the region y = Vx, y = 0, x = 1

A: According to question giveny=xy=0x=1As we know that the volume for solid of revolution between…

Q: y y = x2 + 2 A В 1 2

A: The volume obtained by rotating region between two curves f(x) and g(x) around y=k over the interval…

Q: Calculate the mass of the solid, in the first octant, bounded by the coordinated planes and the plan…

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Q: 13. y? = 5-x, x=0; about x = 5

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Q: 4. Find the volume and centroid generated by revolving the given plane area about y=6x-x^2,…

A: Given:    y=6x-x2   y=x2-2x     y = -1

Q: 7. y' = 4x, x = 4; about x = 4

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Q: ゴー aab

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Q: Find the volume of the solid bounded by the ellipsoid 4 = 1 49

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Q: = 1, 三 a NIU + +

A: Here Let u = x/a, v = y/b , w = z/c Then dx = a du, dy = b dv, dz = c dw So, Required volume V =…

Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y…

A: Please see the attachment

Q: Calculate the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the…

A: Given query is to find the volume of the solid.

Q: Find the volume of the region using cylindrical coordinates.

A: Volume is the amount of space occupied by the closed surface. In this problem, the region is bounded…

Q: Use polar coordinates to calculate the volume of a sphere of radius R.

A: This question is based on application of polar coordinates integration.

Q: find the volume of the solid obtained by rotating region A in Figure 13 about the givenaxis. y = 2

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Q: Compute the volume of W using cylindrical coordinates.

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Q: find the volume of the solid obtained by rotating region A in Figure 13 about the givenaxis. x = −3

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Q: Find the volume of the solid generated when the area bounded by the given curves and lines is…

A: Find the volume of the solid generated when the area bounded by the given curves and lines is…

Q: Find the volume of the solid obtained by rotating the region

A: First draw the graph of common region. y=x3 is represented by blue linex=2 is represented by green…

Q: Refer to the figure and find the volume V generated by rotating the given region about the specified…

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Q: Find the volume generated by y = x^2, x=0 and y = 4 rotated about the y axis. with drawing please.

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Q: find the volume of the solid obtained by rotating region A in Figure 13 about the givenaxis. x-axis

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Q: y y = x² + 2 6. A 2 В 1 2

A: We have to find the volume obtained by rotating region B about x = -3.