find the volumes of the solids generated byrevolving the regions about the given axes. If you think it would bebetter to use washers in any given instance, feel free to do so. The triangle with vertices (1, 1), (1, 2), and (2, 2) about the y-axis

Q: O Find the volume of the solid under the surface z = xy and above the triangle with vertices (1, 1),…

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Q: Let R be a region bounded by the graphs of the equations: y=x2, y=0, x=3 Find the volume of this…

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Q: The base of a solid is the region bounded by the ellipse 4x2 + 9y² 36. Find %3D the volume of the…

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Q: The base of a solid is the triangle in the xy-plane with vertices (0, 0), (1, 0), and (0, 1). The…

A: Given,          The base of a solid is the triangle in the xy-plane with vertices (0, 0), (1, 0),…

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

A: Solution

Q: 2. Suppose that the triangle with vertices (-1,-1), (0, 1) and (1,–1) is revolved about the y –…

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Q: Find the volume of the solid enclosed by the paraboloid z = 2 + x2 + (y − 2)2 and theplanes z = 1, x…

A: The volume between the surfaces and over a region D defined by and is given by the integral . In…

Q: If the region R = {(x, y) | x > 1,0 < y < 1/x} is rotated about the x-axis, the volume of the…

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Q: The base of a solid is the region bounded by the ellipse 4x +9y = 36. Find the volume of the solid…

A: a Given ellipse equation,4x2+9y2=36y2=4-49x2

Q: Find the volumes of the solids Find the volume of the solid generated by revolving the regionbounded…

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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: (a) Find the volume V of the wedge shown in the figure. Top: y + z = 1 Side:

A: In this question we will use basic of calculus i.e application of integration. We will use concept…

Q: (a) Find the volume under the surface z = 3x³ + 3x²y and over the rectangle R = {(x, y): 1 < x < 3,0…

A: we need to find he volume under given surface and over the rectangle.We will solve this problem by…

Q: Find the volume of the pyramid with base in the plane z = -11 and sides formed by the three planes y…

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Q: Find the volume of the indicated region. the tetrahedron bounded by the coordinate planes and the…

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

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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: Find the volume of the solid that lies within both the cylinder x2 + y2 = 1 and the sphere x2 + y2 +…

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Q: Find the volume of the solid bounded by the graphs of the sphere x² + y² +z? =16 and the cylinder…

A: Given solid is bounded by sphere x2+y2+z2=16 and cylinder x+y-22=4 Volume using cylindrical…

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: 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: The base of a solid is the disk bounded by the circle x² + y? = r2. Find the volume of the solid…

A: a) If the cross section perpendicular to x axis is a square, then the solid is a cylinder of height…

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 limited by the graphs of the equations

A: Part (a):

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 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 region that lies inside the sphere x2 + y2 + z2 = 2 and outside the cylinder…

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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: The base of a solid is the region bounded by the parabola y = x2and  y = 2- x2. Find the volume of…

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Q: If the region R = {(x, y) | x 2 1, 0 sys 1/x} is rotated about the x-axis, the volume of the…

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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: Let a and b two real numbers such that a < b. A region R is bounded by a curve C and two different…

A: Given: A region R is bounded by a curve C and two parallel lines to x-axis and C does not cut y-axis…

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

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Q: Determine the volume of the region that lies under the sphere x² + y² + z² = 4, above the plane z…

A: Given: Now,

Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

A: Use volume of solid of revolution formula for finding the volume

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 region enclosed by the cone z = x² + y² and the sphere r2 + y? + z² = 4.

A: Solve for volume

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: Calculate the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the…

A: Given query is to find the volume of the solid.

Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

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Q: use the shell method to find the volumes ofthe solids generated by revolving the shaded regions…

A: Given: x1= y22;   x2= y44-y22   y=0;  y=2Height…

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: The base of a solid is the region bounded by the graphs of y = x², x = 2, and y = 0. a. Find the…

A: The base of the solid is the region bounded by the graphs of  y=x2,x=2 and y=0 (x-axis). Now, Slice…

Q: Find the volume of the solid that is enclosed by the cone z = and the sphere x² + y2 + z2 = 72.

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Q: Find the volume of the solid made when the region in the first quadrant bounded by y = ÷, x = 2, and…

A: According to the given information it is required to find the volume of the solid obtained by…