Q3: Find the volume of the solid enclosed by the parabola y = x² +z? and the cone y = 32 – x² - z2.

Q: Find the volume of the solid above the cone z = Vx² + y? and below the paraboloid z = 20 – x² – y?

A: Given For the given region, the paraboloid z=20-x2-y2 is the upper surface, and the cone z=x2+y2 is…

Q: Find the volume of the solid that lies under the elliptic paraboloid x2/9 + y2/16 + z = 1 and above…

A: Volume in xy-plane

Q: Find the volume of the solid generated by revolving the shaded region abouti хаxis Q 3x+ 5y = 15 5

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Q: Find the volume of the solid that lies under the hyperbolic paraboloid = 3y² – x² + 2 and above the…

A: Integral

Q: Q3 By sketching the graph, find the volume of the solid generated by revolving the region bounded by…

A: The volume of the generated by revolving the region between where and about y-axis is given by,…

Q: The base of a solid is the region bounded by the x-axis and the graph of y V1-z. For the solid, each…

A:

Q: Find the volume of the solid that lies under the elleptic paraboloid x2/9 + y2/16 + z + 1 and above…

A: Given the elleptic paraboloid x2/9 + y2/16 + z = 1  And rectangle R = [-1, 1] x [-3, 3] We have to…

Q: Find the volume of the solid that lies above the cone z = Vx² + y? and inside the sphere x² + y² +…

A: To find the volume of a solid abov the cone  and inside the sphere Firstly find the region in…

Q: Find the volume of the solid above the cone z2= 3(x2 + y2 ), z ≥ 0 and below the sphere x2+ y2+ z2 =…

A: We convert the units in spherical coordinate. The cone is given as,  The sphere is given as, The…

Q: Q3 By sketching the graph, find the volume of the solid generated by revolving the region bounded by…

A:

Q: Find the volume of the solid that lies inside both the cylinder x² + y² = 16 and the sphere x² + y²…

A: Given cylinder and sphere x2+y2=16x2+y2+z2=36 clearly, Here we need to find volume inside both…

Q: Find the volume of the solid generated by revolving the curve y? - x10 – 22 = 41 between a = 0 and x…

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Q: Find the volume of the paraboloid, z = 9 - x² - y², that lies inside the cylinder x² + y² = 4.

A: It is seen that the paraboloid and cylinder both are extended upto negetive infinity of along z…

Q: Consider the solid generated by the surfaces in the 1st octant ?+y?+zZ =4 y?+2 = 2 Find the triple…

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Q: Q.6 Find the volume of the solid generated by revolving the loop of the curve y =x(2-x) about the x-…

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Q: Q3) A- Find the volume of the solid generated by revolving the region Enciosed by the curve (y3v4-…

A: We have to find the volume of the solid generated by revolving the region  enclosed by the curve…

Q: Use the disk method to evaluate the volume of the solid formed by rotating the area between…

A: Given,      Interval [ 2, ∞)

Q: Q3: Find the volume of the solid enclosed by the parabola y = x? + 22 and the coney = 32 — x? — z2,

A:

Q: Q2 Find the volume of the solid in the first octant bounded by the coordinate planes, the plane x =…

A:

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is

A: Given

Q: Q5: Find the volume of the solid bounded by surfaces z = /9- x2 - y2, and z = /25 – x2 - y² and the…

A: Given solid is bounded by Z = 9-x2-y2 and Z = 25-x2-y2 and x2+y2-z2 = 0

Q: A gasoline tank is an oblate spheroid generated by revolving the region bounded by the graph of…

A:

Q: Find the volume of the solid region bounded below by the paraboloid z = 4x2 + y? and above by the…

A:

Q: Q6: Determine the mass of the solid that bounded by the paraboloid 1= 8-(y +x) and the planes z-9,if…

A:

Q: Find the volume of the solid that is enclosed by the cone z = x² + y² and the sphere x² + y² + z² =…

A: Given: Equation of cone z=x2+y2 Equation of sphere x2+y2+z2=2

Q: Find the volume of the solid that lies under the elliptic paraboloid x2/9 + y/16 + z = 1 and above…

A:

Q: Q3 A symmetrical parabolic segment y = 4x(2 -x) rotates around the x-axis as shown in the figure.…

A:

Q: Q2 (a) Find the volume under the surface z = 3x3 + 3x2y and over the rectangle R = {(x,y): 1 < x<…

A:

Q: Q3: Find the volume of the solid that lies above the cone x2 = z2 + y? x = 8 – (z? + y²). and under…

A:

Q: Q5: A- Find the mass of the region cut from the sphere x+y+z=a² by the cone z = √x² + y² if the

A: We have to find the mass of the region cut from the sphere by cone.

Q: d) Find the volume of the solid region bounded by the paraboloid z = 4-x² - 2y and the ху- plane

A: The above of the solid region is calculated as : ∫∫∫Ddv = V In order to calculate the volume of…

Q: (b) Find the volume of the solid generated when R is rotated about the x-axis.

A:

Q: Q3: Find the volume of the solid that lies above the paraboloid z = x² + y², under the plane z=4,…

A:

Q: Find the volume of the solid in revolution as it rotates about the y axis and the function 1. f(x) =…

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Q: Q2/ Find the volume of the solid that lies below the surface given by z-16xy +200 and ies above the…

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Q: 3. Find the volume of the solid that lies under the paraboloid 5z = x² + y², above the xy-plane, and…

A: To find the volume of the solid that is bounded by given curves.

Q: A solid of revolution is generated by rotating the region between the x-axis and the graphs of…

A:

Q: Q3\ Find the volume of the solid generated by revolving the region between the y-axis and the curve…

A:

Q: Use the disk method to find the volume of the solid of revolution bounded by the x-axis and the…

A: Given: The equation of the curve is The region is rotated about x-axis. The volume of solid…

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 20 + x² - y? and above…

A: We have given z = 20 + x2 − y2 and R = [−2, 2] × [0, 4]

Q: Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 9, above the xy-plane, and…

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Q: Find the volume of the solid that lies under the elliptic paraboloid z = y^2 + 8x^2 + 1 and above…

A:

Q: Q4/ find the volume of the solid generated by revolving the shaded region about the x-axis, Use the…

A: Answer is below

Q: Sketch the hypocycloid x2/3 + y2/3 = 1 and find the volume of the solid obtained by revolving it…

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Q: Q3 By sketching the graph, find the volume of the solid generated by revolving the region bounded by…

A:

Q: x2 + y? and the sphere Determine the volume of the solid enclosed by the paraboloid x² + 3y? + 2² =…

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Q: Q5: Find the volume of the solid bounded by surfaces z = /9 - x2 - y2 , and z = /25 - x2 - y? and…

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Q: 5. Find the volume of the solid generated by revolving about the x-axis the smaller area bounded by…

A: Solution :- As per guidelines . I do first only.