The volume of the solid given by the two surfaces is she = 8-3(x? + y*), z = (x² +y?)2 2

Q: Find the volume of the solid in the first octant bounded by the cylinder z = 4 – y? and the plane x…

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Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 – 3y², and the…

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Q: Find the surface area of the portion of the half ball with a radius a which cuts off by the cylinder…

A: To Find: The surface area of the portion of the half ball with a radius a which cuts off by the…

Q: Find the volumes oF the solids geverated by revolving +he regions bounded by the graphs oF the…

A: Given:-  the region bounded by  y=2x2y=0  and x=2rotating about the x-axisusing washer/disk method…

Q: (1 point) The volume of the solid obtained by rotating the region enclosed by y = a², y = 2x, about…

A: y=x2y=2x about line x=2 for point of intersection x2=2xx2-2x=0x(x-2)=0x=0,2

Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

Q: Find the volume of the solid that results when the region enclosed by x = - y² + 7, and x = y + 4 is…

A: We first find the y values of the intersecting points by setting the equations…

Q: The surface area of the solid generated by revolving the straight line 2y = x+1 bounded by x-1, x 3…

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Q: 8. Find the volume of the solid whose base is the semicircle y = V9 – x², where -3 sIS 3, and whose…

A: This question is based on application of integration.

Q: A metal plug has been designed using the intersection of the two cones z = √√x² + y² and √x² + y² +…

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Q: What is the volume of the solid whose 1 30 cross-sections are squares perpendicular to the x-axis…

A: Given: The region bounded by the curves are: y=x and y=x The cross-sections are squares…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: The volume of solid of revolution generated by revolving the area bounded by curve y=x and the lines…

A: The curves given are  y=x2  &  y=0

Q: The volume of the solid generated when the area bounded by the curves x = y? and y² – 2x + 4 = 0 is…

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Q: find volume of solid 3x^2 ,x=1, y=0 about x axis

A: Consider the region bounded by the curves y=3x2,x=1,y=0 as shown in the figure below: Here, the…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: First we graph the region using a graphing calculator  the shaded region is rotating about the y=48…

Q: Graph the solid that lies between the surfaces z =ex cos(x 2 + y 2) and z=2 - x 2 - y 2 for | x|…

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Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 5y and…

A: To find the integral of volume of solid formed by revolving the given region.

Q: Find the volume of the solid that results when the region enclosed by 4x 0, x = 1, and y = 0 is…

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Q: Find the volume of the solid that lies under the plane 4x + 10y - 2z + 15 = 0 and above the…

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Q: 11. Find the volume of the solid generated by revolving the plane region bounded by y = 4x2 and y =…

A: We have, y=4x2y=10x-x2   It is known that volume of the solid is generated by revolving the bounded…

Q: What is the volume of the solid generated when the region surrounded by y = vx, y = 2 and y = 0 is…

A: Given: y=x,  y=2  and  y=0Rotation around y−axis

Q: To find the volume of the solid generated by revolving the region bonded by x = 12(y² – y³) and the…

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Q: 6) Find the volume of the solid enclosed by the paraboloid z = 2--y and the plane z = 2.

A: According to question given that z=2-x2-y2z=-2

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 51 and the upper cone z2 = 3x2…

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Q: Find the volume of the solid bounded above by f(x,y) = 8x?, below by the xy-plane and %3D the sides…

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Q: Find the volume of the solid in the first octant bounded bythe cylinder z=16 -x2 and the plane y=5

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Q: The area enclosed by y = 4x - x^2 and 2y = 2x + x^2 is revolved about the line x = -1. Using a…

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Q: 4. Determine the surface area of the solid obtained by rotating y = v9 – x2, -2 < x<2 about the x -…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the given…

A: Introduction: A solid of revolution is a solid figure formed by rotating a plane curve around a…

Q: What is the volume of the solid R bounded by the x- axis, x = 2, and y = x2 when R is revolved…

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Q: Find the volume of the solid formed by revolving the region enclosed by the closed curve 4x2 +9y² =…

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Q: Compute for the volume of the solid formed bounded by the equations (y- 4)2 = x - 3, x-10, y-4, and…

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Q: What is the volume of the solid formed when rotating the region bounded by f (x) =-x² + 7x – 12 and…

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 7x^5 on the…

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Q: Find for the volume of the solid generated by revolving the region bounded by у %3 3 х?, у%3D0 аnd x…

A: Let,s find the curve and the bounded region The yellow color is mention the bounded region

Q: Find the volume of the solid generated by the region bounded by -x + y² = 8, x = -2y and y = -2…

A: Given , -x+y2=8, x=-2y, y=-2, revolved about x=-10. Find the volume of the solid generated by the…

Q: Find the volume of the solid bounded by surfaces z = /9-x2 - y2 , and z = /25 - x2 - y? and the…

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Q: What is the solid formed when the area bounded by

A: Given: 2x+y=2 The  coordinate axis is revolved about the y axis. To find: What is the solid form.

Q: Find the volume of the solid bounded by the graphs of the equations: z = 3x + 3y?, x - y+1 = 0, 3x +…

A: This question is about application of intergal calculas

Q: 7. Find the volume of the solid under the surface 1 = 3x+ 2y? above 1 < x < 3, 0 < y < 6 using a…

A: Introduction: We know that the volume under the curve z=f(x,y) and over the region R is given by the…

Q: Find the volume of the solid bounded by y=x2+1y=x2+1 and the line y=−x+3y=−x+3, revolved about the…

A: Given curves are y=x2+1 and y=-x+3 and the line y=5 Find the volume

Q: Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2 and the plane x…

A: Given Data The equation of the cylinder is z=12-3y². The equation of the plane is x+y=2.   Let, The…

Q: So, the volume of the solid of revolution is Volume = V3 = (9 - x)2 dx. To find the volume,…

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Q: The region bounded by f(x) = - 2x² + 8x + 24, x = 0, and y = 0 is rotated about the y-axis. Find the…

A: Introduction: When the cross-sectional area is perpendicular to the axis of revolution and the axis…

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the given…

A: This question can be solved using the concept of volume of solid generated by revolving the bounded…

Q: Find the volume of the solid bounded by the surfaces z = 4 – 4(x² + y²) and z = (x² + y²)² – 1.

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Q: Find the volume of the 'ice-cream' that is bounded by x² + y2 + z2 = 10 and the upper cone z2 = 4x2…

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Q: Find the volume of the solid enclosed by the paraboloids z=16(x^2+y^2) and z=8−16(x^2+y^2)

A: To calculate the volume of the region contained between the two given surfaces

Q: Find the volume of the solid in the first octant bounded by the parabolic cylinder z= 25 - x and the…

A: Since we are considering only in the first octant so lower limit of both x and y will be zero.…