Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 3.

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 that lies under the hyperbolic paraboloid z = 3y² – x² + 2 and above…

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Q: Calculate the volume of one of the wedge-like objects formed by cutting the cylinder x²+9y²=a² with…

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Q: Find the centroid of the region with the indicated boundaries: The parabola y² = 4x, the Y-axis,…

A: We use the formula  x=MyM=∫abxfx-gxdx∫abfx-gxdxy=MxM=∫ab12fx2-gx2dx∫abfx-gxdx Now, fx=4, gx=4x, a=0,…

Q: Find the volume beneath the paraboloid z = 25 − x2 − y2 and above the xy-plane

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Q: Find the volume of the ellipsoid =D1 in positive octant Once

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Q: Find the Volume cutoff from the cylinder x2 +y2 = 9 by the planes z = 0 and z = 5.

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Q: Find the volume of the shaped body bounded by the z = 3x2 + 3y2 and          z = 4 - x2 - y2…

A: We have to Find the volume of the shaped body bounded by the z = 3x2 + 3y2 and        z = 4 - x2 -…

Q: Find the volume of the solid enclosed by the paraboloids: z = 2x2 + y2 and z = = 27 – x² – 2y2. 5.

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Q: Find the volume of the solid bounded by the paraboloids z 9 + 3x2 + 3y and z = 7 - 3x? – 3y?

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Q: Find the volumes of the solids whose bases are bounded by the graphs of y = x + 3 and y = x² - 3,…

A: So points are ( -2 , 1 ) and ( 3, 6 )

Q: Find the volume of the tetrahedron bounded by the plane z=4-4x-2y and the coordinate planes. I

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Q: Find the volume of the solid enclosed by the paraboloids z=9(x2+y2) and z=2−9(x2+y2)

A: By using polar coordinates we will find the volume

Q: find the centroid of volume if the volum is equal to 7/15 π

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

A: We need to evaluate volume.

Q: Find the volume of the pyramid with base in the plane z=−5 and sides formed by the three planes y=0…

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Q: Find the centroid of the region in the first quadrant bounded by the x-axis, the parabola y2 = 2x,…

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

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Q: Find the volume of the pyramid with base in the plane z = and sides formed by the three planes y -9…

A: To solve the following problem

Q: Find the volume of the solid in the first octant bounded by the coordinate planes, the cylinder x2 +…

A: Consider the provided information, The cylinder x2+y2=4. And the plane z+y=3. Find the volume of the…

Q: Find the volume limited by the graphs of the equations

A: Part (a):

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

A: Please see the explanation below

Q: Find the volume of the solid formed by two paraboloids: z1=x2+y2andz2=1−x2−y2.

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Q: Find the volume of the solid enclosed by the paraboloids z z = 18 – 4 (x2 + y²). 4 (x² + y²) and

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Q: find the center of mass of a thin plate of constantdensity d covering the given region The region…

A: Given :                 y = 2x2 - 4x  and y = 2x - x2    Graph :…

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 dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z…

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Q: Find the volume of c such that the area of the region bounded by the parabolas y = 16x2 - c2 and y =…

A: Given parabolas are y1=16x2-c2y2=c2-16x2 The area between the given parabolas is 1283

Q: Find the volume of the solid enclosed by the paraboloid z = 5 + x2 + (y - 2)2 and the planes z = 1,…

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

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Q: 6. Find the volume inside the paraboloid z = 9-x² - y², outside the cylinder x² + y² = 4, above the…

A: Relation between rectangular and polar coordinate  x=rcosθy=r sinθx2+y2=r2θ=tan-1yxdxdy=rdrdθ

Q: Find the volume of the solid enclosed by the paraboloids z = 16 (x² + y²) and z = 8 − 16 (x² + y²).

A: We have to find the volume of the solid enclosed by the paraboloids z=16(x2 +y2) and z=8−16(x2 +y2).…

Q: Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic…

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Q: Find the volume of the region bounded above by the paraboloid z = x² + 2y² and below by the square…

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Q: Find the volume of the solid enclosed by the paraboloid z = 3 + x² + (y – 2)2 and the planes z = 1,…

A: Given z=3+x2+(y-2)2 and the planes z=1, x=-2,x=2,y=0 and y=2.

Q: Find the volume of the largest closed rectangular box in the first octant having three faces in the…

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Q: 2Ay-3-2r

A: In this question we find volume of the shaded region that is revolved arround y-axis.     Here i…

Q: Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x =…

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Q: Find the volume of the solid enclosed by the paraboloids z = 9 (x² + y) and z = 18 – 9 (x? + y).

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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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 pyramid with the base in the plane z= -5 and the Sides formed by the three…

A: To find the volume of the pyramid

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

A: To find the volume of the solid the lies under the below hyperbolic paraboloid and above the…

Q: Find the volume of the solid enclosed by the paraboloid z = 5 + x + (y - 2)2 and the planes z = 1, x…

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Q: Write six different iterated triple integrals for the volume of the tetrahedron cut from the first…

A: Given plane,

Q: Find the volume of the solid enclosed by the paraboloids: z = 2x² + y? and z = 27 – x2 – 2y². %3D |

A: The given equation of the paraboloids are: z=2x2+y2 and z=27-x2-2y2 Find the volume of the solid…

Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

A: According to the given information it is required to find the dimension of right circular cylinder…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: Find the volume of the wedge cut from the cylinder x2+y2=1 by the planes z = -y and z = 0.

A: The Volume of the wedge, where D is the solid and R is the region, is calculated as,

Q: 2. Find the volume of the wedge cut from the 1-st octant in R³ by the surface z = 4-1 - y.

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