Find the volume of the region enclosed by the cylinder x2 + y2 = 4 and the planes z = 0 and y + z = 4.

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = 15 – x, y…

A: Please refer the attached image for complete solution.

Q: Find the volume of the region above the xy-plane, inside the cone z = 6 – Væ² + y² and inside the…

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: Find the volume of the region between the planes x+y + 2z =2 and 2x + 2y +z = 4 in the first octant.

A: Find the volume of the region between the planes  x +y + 2z = 2 ......... (1)  and  2x + 2y +z =4…

Q: Find the volume of the solid obtained by rotating the region bounded by 2y = x², %3D y = 2, y = 8…

A: According to the given information, it is required to find the volume of the obtained solid.

Q: Find the volume of the region bounded above by the elliptical paraboloid z = 10 + x2 + 3y2 and below…

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Q: Find the volume of the region above the xy-plane, inside the cone z = 18 – Vx² + y² and inside the…

A: We have to find the volume of the region bounded by the xy-plane, inside the cone, and inside the…

Q: Find the volume of the solid obtained by rotating the regionbounded by y = x 3 , y = 8 ,and x = 0…

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Q: Find the volume of the region enclosed by the cylinder x2 + y2 = 4 and the planes z = 0 and x + y +…

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Q: Find the volume of the solid. y=x2, x=0; x=2, y=0, about the x-axis

A: use the volume of solid of revolution formula,

Q: Find the volume of the region enclosed by the cylinder x^2 + y^2 = 4 and the planes z = 0 and x+ y +…

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Q: Find the volume of the tetrahedron bounded by 2x−y+z = 4 and the coordinate planes.

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Q: Find the volume of the solid obtained by rotating the region bounded by y = x² , y = 0, and x = 5,…

A: Shells method

Q: Find the volume of the solid obtained by rotating the region bounded by y = x* , y = 0, and a = 4,…

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Q: Find the volume of the region en-closed by the cylinder x2 + y2 = 4 and the planes z = 0 and x + y +…

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Q: Use the method of cylinders to determine the volume of the solid obtained by rotating the region…

A: Given that, y=2x+1, y=3, x=4 and the line y=10

Q: Find the volume of the solid that results when the region bounded by y = Vā ,y = 0 and æ = 4 is…

A: Volume

Q: Find the volume of the first octant region bounded by the coordinate planes and the parabolic…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 8x, x = 1, and y = 0,…

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Q: Find the volume in the first octant bounded by the cylinder x² +y = a² 2a and the lane z = x + v.

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Q: Find the volume of the region that lies inside the sphere x2 + y2 + z2 = 2 and outside the cylinder…

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Q: Find the volume of the solid obtained by rotating the area in the first quadrant bounded by y = x^2,…

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Q: Find the volume of the tetrahedron bounded by the four planes x=0,y=0,z=0, and 2x+2y+x=4?

A: The equation of the plane 2x+2y+z=4  can be rewritten in the form  z=4-2x-2y let z=0, 0=4-2x-2y…

Q: Find the volume of the solid obtained by rotating the region bounded by y = 2x?, x = 1, and y = 0,…

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Q: Find the volume of the solid generated when the region enclosed by y = Vx + 2, Y = /5x, and y = 0 is…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = x^3, y = 8, and x = 0…

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Q: Find the volume of the region enclosed by z = 1 – y and z = y² – 1 for 0 < x < 42. - V =

A: To find the volume of the region enclosed by z=1-y2 and z=y2-1 for 0≤x≤42

Q: Find the volume of the solid which is (a) bounded by x+ y+z = 4 in the first octant.

A: As per our guidelines we are supposed to solve only one question. For the solution follow the next…

Q: Find the volume of the region bounded by y=x^3 and y=x rotated about the x-axis.

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 9x?, x = 1, and y = 0,…

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Q: find the volume,The region bounded in back by the plane x = 0, on the front and sides by the…

A: Given

Q: Find the volume of the region bounded by y = Vx and y = x rotated about the x-axis.

A: The graph is where red curve represents y=x and blue line represents y=x.

Q: find the volume ,The region between the planes x + y + 2z = 2 and 2x + 2y + z = 4 in the first…

A: Given planes are

Q: Find the volume of the solid obtained by rotating the region bounded by Y x2 , y = 0, and = x = 4,…

A: find the volume by using shell method. The Shell Method:-                                      If R…

Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane y + z…

A: Given that the region in the first octant bounded by the coordinate planes, the plane y+z=2 and the…

Q: Find the volume of the solid lying below the graph of z = x* + xy + y³ and above the rectangle 1 < x…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 4x², x = 1, and y = 0,…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 6x?, x = 1, and y = 0,…

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Q: Find the volume of the region enclosed by z = 1 - y² and z = y² - 1 for 0 < x < 42. V =

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Q: Find the volume of the region bounded above by the plane z = y/2 and below by the rectangle R:…

A: Given, plane We have to calculate the volume of the bounded region.

Q: Find the volume of the region bounded by z = x2,0 <x < 7, and the planes y = 0, y = 2, and z = 0.

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 2a², x = 1, and y = 0,…

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Q: Find the volume of the region bounded above by the elliptical paraboloid z = 16 - x2 - y2 and below…

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Q: find the volume of the region in the first octane bounded by the coordinant planes, the plane y + z…

A: See the details solution in below

Q: Find the volume of the solid obtained by rotating the region bounded by = 5a?, 5x², x = 1, and y 0,…

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x5,…

A: We first sketch the region using a graphing calculator.

Q: Find the volume of the solid obtained by rotating the region bounded by æ = 8y°, y = 1, x = 0, about…

A: Given:       x=8y2 , y=1, x=0

Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane x + y…

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Q: Use the disk method to find the volume when the region bounded by y = ex + 1, x = 0, x = 1, and y =…

A: y=ex+1,  x=0,  x=1  &amp;  y=0.

Q: Find the volume of the region bounded by y= √x and y=4x rotated about the y-axis.

A: