Find the volume of the solid generated by revolving the pentagon with vertices (1, 0), (2, 2), (0, 4), (-2, 2) and (-1, 0) about the x-axis.

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: 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 tetrahedron in the first octant bounded by the coordinate planes and the…

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Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

Q: Find the volume of solid lying in the first octant bounded by the graphs of : z = 4 – x2 – y² , y =…

A: The volume of the solid in first quadrant is given by: V=∫ab∫cdf(z)dydx Now, find the range of the…

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

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Q: Find the volume of the solid in the first octant bounded by the coordinate planes, the plane x = 3,…

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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 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: Find the volume of the solid that lies under the plane 2x−4y+5z=18 and above the rectangle R={(x,y)…

A: Given, Plane is 2x-4y+5z =18 And 1≤x≤3  2≤y≤4

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

A: Given: y=1-x2 and y=x2-1

Q: Find the volume of the region under the surface z = corners (0, 0, 0), (6, 0, 0) and (0, 3, 0). 824…

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Q: Use the Theorem of Pappus to find the volume of thegiven solid. The solid obtained by rotating the…

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Q: Find the volume of the solid above the triangle with vertices (0, 0), (1, 0) and (1, 2), below the…

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Q: Calculate the volume of the solid bounded by the cone z2=x2+y2 and the cylinder x2+y2=4

A: Explained below

Q: Calculate the volume of the solid bounded by cone z2=x2+y2 and cylinder 4=x2+y2.

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Q: Determine the volume of the solid lying under the elliptic paraboloid z = 6y² – 2x² + 3 and above…

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Q: Find the volume of the solid that is bounded by the cylinder z = 4x2, on the sides by the cylinder…

A: Let's find volume of solid.

Q: Find the volume of the solid obtained by rotating about

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Q: Find the volume of the solid bounded by the ellipic paraboloid z = 3 + 4x2 + 2y², the planes x = 2…

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

A: Given- 1,0,00,2,0 and 0,0,3 To find- The volume of the solid in the first octant bounded by the…

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: Find the volume of the solid bounded from up by surface f (x,y) = 2x + y2 and from below by the…

A: According to question, surface :f(x, y) = 2x+ y2,Traingle vertices : 0, 2, 0, 0 and 3, 2

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

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Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

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Q: Find the volume of solid lying in the first octant bounded by the graphs of : z = 4-x2-y2, y= 2-2x2,…

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: We first sketch the region using a graphing calculator. The shaded region will rotate about the…

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

A: The objective is to find the volume of the tetrahedron in the first octant that is bounded by the…

Q: Find the volume of the solid in the first octant bounded bythe cylinder z=16 -x2 and the plane y=5

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Q: Find the volume of the solid in the first octant by bounded by the plane 3x +42 = 12, y = 2 and the…

A: Volume bounded by thefirst octent

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

A: The solid enclosed by the parabolic cylinders  y=1-x2, y=x2-1and the planes  x+y+z=2,  5x + 5y − z +…

Q: 5. y = 4x – x², x = 0 , y = 4 , revolved at y axis -

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Q: For the solids of revolution, how do I know when to add or subtract from the axis of revolution such…

A: For the solids of revolution, find the volume using disk, washer and cylindrical shell method.

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

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Q: Find the volume of the solid bounded by the graphs of the equations: z = 3x + 3y?, x - y+1 = 0, 3x +…

A: This question is about application of intergal calculas

Q: Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2 and the plane x…

A: Given Data The equation of the cylinder is z=12-3y². The equation of the plane is x+y=2.   Let, The…

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. y=9-x2, y=0, about the x-axis

A: The given solid is bounded between the curve y=9-x2, y=0,  rotating about the x-axis. Volume of the…

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 region bounded above by the elliptical paraboloid z = 16 - x2 - y2 and below…

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Q: 3. Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

A: Given

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

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Q: Compute the volume of the solid bounded above by z = 8xy° and below by the triangle with vertices

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

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

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Q: Find the volume of the solid enclosed by the paraboloids z=16(x^2+y^2) and z=8−16(x^2+y^2)

A: To calculate the volume of the region contained between the two given surfaces