Calculate volumes and areas of solids bounded by planes: a) $x=0, y=2, z=-1, x+y+z=6$

Q: Find the volumes of the solids generated by revolving the regionsbounded by the lines and curves…

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Q: Find the volume of tetrahedron with vertices (0,0,0),(1,0,0),(0,1,0)and (0,0,2) by triple integral?…

A: We have to find the volume of the tetrahedrane with vertices 0,0,0, 1,0,0, 0,1,0 and 0,0,2 by triple…

Q: Find the volume of the intersection of the unit ball {(x, y, z) : x² + y² + z2 < 1} and the cylinder…

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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 volume of the solid obtained by rotating the triangle with the vertices A(0,0), B(4,4) and…

A: Solution

Q: By using either a double or triple integral, find the volume of the tetrahedron with vertices…

A: To determine :- The volume of the tetrahedron with vertices 0,0,0 , 1,0,0 , 0,1,0 , 0,0,1.

Q: Find the volume of the solid generated by revolving the region enclosed by the triangle with…

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Q: Find the volume of the solid bounded by the planes given below

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Q: z = 0, y = 1, у %3D1, z = x² + y? y = x².

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Q: Find the volumes of the solids generated by revolving the regionsbounded by the lines and curves…

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Q: Find the volume of the intersection of the unit ball {(x, y, z) : x²+y + z² < 1} and the cylinder…

A: We are given two solids and all space between two planes. x2+y2+z2≤1, the unit sphere. x2+y2≤14,…

Q: Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 5), and (5, 0).…

A: Sketch the base of the solid as follows.

Q: Use the shell method to find the volumes of the solids generated byrevolving the regions bounded by…

A: We have to use the shell method to find the volume of the solids generated by revolving the regions…

Q: 2. bounded by the axis of the region Volume of the body of rotation created by rotating it Oround ?

A: Given that  y = 1 -x2, x =0 , y = 0   x2 = 1- y The limits of y :-  from y = 0 to y = 1

Q: Use the Theorem of Pappus to find the exact volume of a general cone created by rotating a triangle…

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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 under the plane z= 2x + y and over the rectangle R = {(x, y) : 3<x< 5,1< y< 2

A: Given Rectangle  R=x,y:3≤x≤5,1≤y≤2

Q: Find the volumes of the solids generated by revolving the regionsbounded by the lines and curves…

A: Consider the following figure:

Q: Compute the volume lying inside the sphere x2 + y? + z2 = 46 but outside of x² + y? = 21.

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Q: Find the volume of the solid bounded by the planes given below y = 0, y = 1, x=0, x= 1, z = 0 and…

A: Given, y=0,y=1,x=0,x=1,z=0 x+y+z=3 This implies, z=3=x-y Use the formula, volume of the solid…

Q: By using either a double or triple integral, find the volume of the tetrahedron with vertices…

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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…

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Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder a? + y = 64 and…

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

Q: Find the volume of the region cut from the solid sphere ρ≤ a by the half-planes θ = 0 and θ = π/6 in…

A: Find the volume of the region cut from the solid sphere.

Q: Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 4), and (2, 0).…

A: Given vertices of the triangular base is 0,0, 0,4 and 2,0. We know the equation of the line passing…

Q: Use the shell method to find the volumes of the solids generated byrevolving the regions bounded by…

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Q: Find the volumes of the solids generated by revolving the regionsbounded by the lines and curves…

A: y=x2, y=0 x=2 Volume V will be- V=π∫01x2dx

Q: Determine the volume of a four dimensional unit sphere: x, =r sin 8, sin 8, cos p, x, =r sin 0, sin…

A: The given problem is to find the volume of four dimensional unit sphere, we have to set up an…

Q: find the volume,The finite region bounded by the planes z = x, x + z = 8, z = y, y = 8, and z = 0

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Q: Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y +z = 7.

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Q: Find the volume V which lies inside the sphere x^2+y^2+(z−4)^2=16 and outside the sphere…

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Q: Find the volume (in m3)  of a right truncated triangular prism with a triangular base whose sides…

A: Please follow step 2nd .

Q: Let V, and V, be the volumes of the solids that result when the plane region bounded by y = 1/x, y =…

A: Given that curves are                                         y=1x, y=0, x=18 and x=c&gt;18 V1 and…

Q: Calculate the volume of the solid bounded inferiorly by the sphere (image 1) and superiorly by the…

A: Let, E be the region bounded below by the sphere x2+y2+z2=2z and bounded above by the cone z=x2+y2

Q: Find the volumes of the solids formed when the region bounded by y = 0 and y = 1/x, between x = 1…

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Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the region…

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Q: = 1, 三 a NIU + +

A: Here Let u = x/a, v = y/b , w = z/c Then dx = a du, dy = b dv, dz = c dw So, Required volume V =…

Q: Find the volume bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 2. 1. V 3 4 2. V 7 4 3. V…

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Q: Use the shell method to find the volumes of the solids generated byrevolving the regions bounded by…

A: The Volume of the solid using shell method is given by,…

Q: Find the volume of the solid bounded by the planes x 0, y z = 1 0, z = 0, and x + y

A: To calculate the volume of the three dimensional region given

Q: Use the Theorem of Pappus to find the exact volume of a general cone created by rotating a triangle…

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Q: Compute the volume lying inside the sphere x? + y? + z? = 37 but outside of x² + y? = 21.

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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: Find the volume bounded by the cylinder z=y², y=x² and the planes z=0, y=4.

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Q: 1. Use Pappus' Theorem to find the volume V of the torus generated by revolving a circular region of…

A: There are two Theorem by Pappus 1st for surface area of revolution and 2nd for volume of revolution…

Q: Find the volume generated by y = x^2, x=0 and y = 4 rotated about the y axis. with drawing please.

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Q: Find the volume of the region that is bounded by the spheres x2 + y? + z2 = 1, x2 + y? + z2 = 36 and…

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