Find the volume of the solid whose base is bounded by the circle x2 + y? = 36 and whose cross sections perpendicular to the x-axis are equilateral tr

Q: Find the volume of the solid obtained by rotating the region bounded by x = 2 – y? and x = y about…

A: Consider the given functions. x=2-y2 and x=y Put both the functions equal.…

Q: Find the volume generated by revolving the region bounded by y=−x^4+3x^3, y=0  revolving about the x…

A: The given problem is to find the volume generated by revolving the region bounded by given curves…

Q: Determine the volume of the solid formed by revolving the area bounded by x2 = 4y– 4, x= - 2, x=3…

A: Given region R is bounded by x2=4y-4x=-3x=3 Region R is shown below

Q: Find the volume formed by revolving about the line y = 2a, the area bounded by that line, the curve…

A: As per rule of Barbtleby we can solve only one question at a time and we can solve only three…

Q: Find the volume of the solid whose base is given by 9. whose cross-sections perpendicular to the…

A: We will first find the area of cross section. Then integration of Area will be required volume of…

Q: Find the volume of the solid whose base is the semicircle y = √9 - x² where -3 ≤ x ≤ 3, and the…

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Q: The area bounded by y = 2x² - x³, and y=0 is revolved about x=0. Find the volume of the solid…

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Q: Find the volume of the solid generated when the region enclosed by y = \2x + 8, y = x, x = 0 is…

A: If y=f(x) is a function, then the independent variable x is called the input of the function, and…

Q: 8. Find the volume of the solid whose base is the semicircle y = V9 – x², where -3 sIS 3, and whose…

A: This question is based on application of integration.

Q: Find the volume generated by rotating the region between the graphs of x = sqrt (y) , x = 0, and y =…

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Q: Find the volume of the torus generated by revolving the region bounded by the graph of the circle…

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Q: Find the volume of the solid generated when the region enclosed by y = sqrt(x), y = 0, and x = 49 is…

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Q: Find the volume generated by revolving the area bounded by y = 1 - x³, OX and OY about the x-axis.

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Q: Find the volume of the solid whose base is an isosceles triangle (with base 6 meters and sides 5…

A: Given a solid whose base is an isosceles triangle (with base 6 meters and sides 5 meters) and whose…

Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 16 and whose cross…

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Q: Find the volume when the region bounded by y = 2x², x = 0, x = 4, and y = 0 is revolved about the…

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

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Q: If the region enclosed by the y-axis, the line y=2 and the curve y=sqrtx is revolved about the…

A: Proceed as shown below...

Q: Find the volume of the solid generated when the region bounded by y = 9 – x and y = 2x + 6 is…

A: To find the volume of solid generated by revolving around the x axis

Q: Derive the formula for the volume of a right circular cone of height h and radius r using an…

A: Given information:

Q: Find the volume generated by revolving the region enclosed by x -y and y=x+2 about у-аxis.

A: We have to find the volume.

Q: In order to find the volume obtained by revolving the region enclosed by y = Vxe-* and y =…

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Q: Derive the formula for the volume of a sphere by revolving about the x-axis, the region bounded by…

A: We have to derive the formula for the volume of a sphere by revolving about the x-axis, he region…

Q: Find the volume of the solid generated when the region bounded by y= 9x and y 27x is revolved about…

A: Given curves are y=9x   ....1 and y=27x  ...2

Q: Find the volume of the solid generated by revolving about the line x = 2, the area bounded by y =…

A: The equation of the curves are  C1: y = x2C2: x= 2C3: y = 0 The axis of the revolution is x = 2 To…

Q: Find the volume of the solid whose base is bounded by the given function with the indicated cross…

A: 1. Given: x2+y2=4, quarter-circlesx=±2 are the limitsy=4-x2volume =π∫aby2dx

Q: Find the volume of the solid whose base is the region enclosed by y=x^2 and y=4, and the cross…

A: Given: Region enclosed by y=x^2 and y=4. And the cross sections perpendicular to the y-axis are…

Q: What is the volume in the first octant bounded by x2 = 16 – y and z + y = 16.

A: Given curves are

Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

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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: y = x² – 3x; y + x = 0 about the x-axis

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Q: . Find the volume of the solid whose base is the region bounded by the semicircle y = 1– x² and the…

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Q: Find the volume obtained by rotating the area bounded by y=x^4 and y=1 around the line y=8

A: Graph y = x4, y = 1 and y = 8 to find the boundary points as follows.

Q: What is the volume generated when the area bounded by y=2x2+1; x=1; x=2 is revolved about the line…

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Q: Find the volume of the first octant region bounded by the coordinate planes and the parabolic…

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

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Q: The axes of two circular cylinders of radius a intersect at right angles. Show that the volume…

A: 8∫0ady∫0a2-y2dx∫0a2-y2dz = 8∫0ady∫0a2-y2dx (a2-y2)8∫0ady∫0a2-y2dx∫0a2-y2dz  =8∫0ady…

Q: Find the volume of the cone generated by revolving about the y-axis the area bounded by the line 2x…

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Q: Find the volume of the solid of revolution bounded by the circle +y = 16, and the lines 0 and

A: To find: Volume of the solid

Q: Find the volume of the cone generated by revolving about the y-axis the area bounded by the line 2x…

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Q: Find the volume formed by rotating the region enclosed by: y = x³ + 1, the y-axis, and y = 9 about…

A: We will use the disk method to evaluate the volume of the solid of revolution.

Q: Determine the volume of the solid formed by revolving the area bounded by x2 + y? = 25 and x + y=5…

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Q: Determine the volume generated by revolving the region in the first quadrant bounded by the curves…

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Q: Find the volume obtained when the circle of radius 1 withcenter (1, 0) is rotated about the y-axis.

A: We have to find volume obtained when the circle of radius 1 with center (1,0) is rotated about the…

Q: Find the volume of the solid generated when the region enclosed by y = sqrt(x+1), y = sqrt(5x), and…

A: The volume of the region bounded by the curves y1(x) and y2(x) is given by the formula…

Q: Find the volume of the solid generated when the region enclosed by y = sqrt(2x + 8), y = x, x = 0 is…

A: Given :     To 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 generated by revolving the area bounded by   xy=4, x=1, x=4 and the x-axis about the…

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Q: Find the volume generated by revolving the area bounded by : 2, x = 5, and Ж — x3 + 9x² + 18x y = 0…

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Q: Find the exact volume generated by revolving the region bounded by f(x) = 2x^2 + 10 and g(x) = 4x +…

A: The volume generated by revolving the region by line y= 10 The given functions are fx=2x2+10 and…