3. Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (1,0,0), (0, 2,0) and (0,0, 3).

Q: 8. Obtain the volume of the solid which is bounded by a circular paraboloid z= x +y´, cylinder x +y…

A: The solid is bounded by the curves, This represent that the solid is in first octant only.

Q: 3. Find the volume of the tetrahedron in the first octant that is bounded by the three coordinate…

A: Given the equation of the plane, z=5-2x-y  ⋯⋯(1) Rewriting equation (1), 2x+y+z=5  ⋯⋯(2) At z=0,…

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: 2 Find the volume of the region between the ellipsoid (=) = 1 and the plane 4 8. - | א + నా | co

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Q: Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

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Q: 5. Find the volume of the tetrahedron bounded by the coordinate planes and the plane 3x + 6y + 4z -…

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Q: Find the volume of the wedge cut from the first octant by the cylinder x? + y² = 1 and the plane 2x…

A: We have to find the volume of the wedge cut from the first octant by the cylinder x2+y2=1 and the…

Q: Find the volume of the region bounded above by the elliptical paraboloid z = 8 -3x-5y and below by…

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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: Use the Theorem of Pappus to find the exact volume of a general cone c with vertices (0, 0), (3, 0),…

A: Step:-1 Pappu's Theorem:- According to this theorem, the Volume V of a solid of revolution generated…

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 paraboloid z = 4 + x2 + (y – 2)2 and the planes z = 1,…

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Q: 3. Find the volume of the tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + %3D y + 2z =…

A: Will use the triple integration to find the volume of the tetrahedron which is bounded by the given…

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

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Q: Use the Theorem of Pappus to find the exact volume of a general cone created vertices (0, 0), (1,0),…

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Q: Find the volume of the given solid. Under the surface  z = 9xy  and above the triangle with…

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Q: Find the volume enclosed by the cy linder (x-1) ty²=1 and the sphere x² +y²7z²=L4.

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

A: Part (a):

Q: Find the volume of the prism whose base is the triangle in the xy plane bounded by the x -axis and…

A: Given -  A prism whose base is the triangle in the x-y plane bounded by the x -axis and the lines y…

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

A: To Find: Volume of the largest closed rectangular box in the first octant having three faces in the…

Q: Find the volume of the solid generated by squares whose bases are bounded by the graph of y= 1/x…

A: Given y=1x   x=1 to x=3We know that the volume for solid of revolution for a curve is the volume…

Q: Find the volumes of the solids whose bases are bounded by the circle x^2+y^2=4, with the indicated…

A: Given, x2+y2=4 Part a: We have, x2+y2=4⇒y2=-x2+4⇒y=±4-x2 Now we find the area to use in finding the…

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

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Q: A, Find the volume between the paraboloid z = 9 – x² – y² and z = 5. B, Use an iterated integral to…

A: A. The equation of the paraboloid z = 9 - x2 - y2 and the equation of the plane z = 5.   We plot the…

Q: 44. Find the volume of the solid bounded above by the surface z = 1+xy and below by the triangular…

A: In mathematics, we study two types of figures, one is curvilinear while the other is…

Q: Find the volume of the given solid. Under the surface z = 6xy and above the triangle with vertices…

A: Given: z=6xy A triangle with vertices (1,1),(4,1),(1,2)

Q: Find the volumes of the solids whose bases are bounded by the graphs of y = x + 1 and y = x² - 1,…

A: AREA OF SQUARE=side×side Area of rectangle=Length×breadth

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 region bounded above by the elliptical paraboloid z = 6 - 2x² - 2y² and below…

A: We will use limits of x,y,z to create a triple integral to represent volume and then solve it

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

A:

Q: Find the volume of the given solid. Under the surface z = 7xy and above the triangle with vertices…

A: Given surface is z = 7xy  And region is above the triangle with vertices (1, 1), (4, 1) and (1, 2).…

Q: 7. Determine the volume of the region that lies under the sphere x² + y² +2²=9, above the plane z =…

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Q: 9. Find the volume of the solid in the first octant enclosed by the surface z = x? and the four…

A: Volume = ∫02∫03∫0x2dx dy dz                 =∫02dx∫03dy ∫0x2dz…

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: What is the volume of br^3 of the region bounded by the z=9-x^2-y^2 paraboloid, the xy plane, and…

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

Q: Find the volume of the region of R^3 bounded by the paraboloid z=x^2+y^2 and by the planes…

A: Concept: Let us take D to be a bounded, closed space region. Let a and b represent real numbers,…

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 volumes OF the solids gewerated by revolving +he regions bounded by the graphs oF the…

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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: Find the volume of the largest box, with one corner at the origin and the opposite corner at a point…

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Q: Find the volume of the wedge cut from the first octant by the cylinder z=63-7y and the plane x+y=3

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Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is 32 3 9. 2 O…

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

A: Volume of box = xyz Surface area = 2xy+ 2yz+2zx

Q: Determine the volume of the largest rect an gu lar box in the first oct ant with three faces in the…

A: Given: The volume of the largest rectangular box is to be determined based on the first octant with…

Q: The volume of the tetrahedron bounded by the plane * ++ = :1, {a, b, c > 0} and the coordinate a…

A: Volume of the figure will be given by integral - V = ∫∫∫dzdydxLet's find limits of z,y and x - Given…

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

A: