Show that the volume common to the surfaces 2 p2+z=4ax and x+y?=2ax is (3r+8)*. 3

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 – 3y², and the…

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

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Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 : = 35 and the upper cone z2 =…

A: The given problem is to find the volume of the ice cream that is bounded by given surfaces. Given…

Q: Find the volume of the solid generated by revolving the area bounded by x2 - 2kx - 2ky + k = 0 and…

A: Given curves are:  x2-2kx-2ky+k2=0 2x-2y+k=0 The area bounded by them is revolving about the line…

Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 2ky + k² = 0 and…

A: To calculate the volume of the solid obtained by rotating the region bounded by the curves y=fx and…

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 of the solid generated when the region bounded by x = - sqrt(4y) . y = 4 and x= 0 is…

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Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and…

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Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and…

A: Using cylindrical shell method

Q: 22 Find the Volume of the Solid of revolution bound al by the circuit x*+y=16, aud the lineSX=0 and…

A: Equation of the circle is given as x2 +y2 = 16 x2 +y2 = 42 Where radius of the circle r is 4 unit…

Q: Find the volume of the solid generated by revolving the area bounded by x- y2 + 6y-9 0 and x- y-9 =…

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Q: Find the volume of the region bounded above by the paraboloid z = 9 - x2 - y2, below by the…

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Q: Find the volume of the solid generated when the region bounded by y = 4x and y = 16VX is revolved…

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Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 95 and the upper cone z2 = 4x2…

A: We have to find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 95 and the upper…

Q: Find the volume of the solid that is bounded above by the cylinderz = x2 and below by the region…

A: Given, bounded region z=x2, y=2-x2, y=x region can be define as ∫∫x2dxdy now region is y=2-x2, y=x…

Q: Find the volume of the solid generated by revolving the area bounded by x - y² + 6y - 9 = 0 and x -…

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Q: Calculate the volume of the solid in the first octant bounded by the plane y = 4 and the cylinder z…

A: Volume is calculated using triple integration. Here x varies from 0 to 2 , y from 0 to 4 and z…

Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 3ky + k² = 0 and…

A: Given curves are:  x2-2kx-3ky+k2=0 3x-3y+k=0 The area bounded by them is revolving about the line…

Q: 3. Find the volume of the solid formed by y = √√4sin(x) bounded by x = 0 revolved about the x axis…

A: According to the question we need to find out the volume of revolution of the curve.

Q: Find the volume of the solid generated by revolving the - area bounded by x² − 2kx − 3ky + k² = 0…

A: The given curves are  x2-2kx-3ky+k2=0                 …13x-3y+k=0                 …2 The given line…

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 in the first octant bounded above by the paraboloid z = 9 – x² – y? and on the sides…

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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 bounded by x + y2 = 3z and x2 + y2 = 6x

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

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Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 4ky + k² = 0 and…

A: Given curves are:  x2-2kx-4ky+k2=0 4x-4y+k=0 The area bounded by them is revolving about the line…

Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 4ky + k? = 0 and…

A: Given curves are:  x2-2kx-4ky+k2=0 4x-4y+k=0 The area bounded by them is revolving about the line…

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 51 and the upper cone z2 = 3x2…

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Q: Find the volume generated by revolving the area bounded by y² – 4y – 4x + 4 = 0 and x = 1 about the…

A: Volume bounded by the region along x=1

Q: Compute for the volume of the solid formed bounded by the equations (y- 4)2 = x - 3, x-10, y-4, and…

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Q: Find the volume of the solid that is bounded by Y3D0 2.x +3y +5z = 30

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Q: The volume of the solid obtained by rotating the region enclosed by y = x², y = 3x, about the line y…

A: Given: y=x2 ; y=3x   Now find the point of intersection between the curve and line;…

Q: Find the volume of the solid generated by the region bounded by -x + y² = 8, x = -2y and y = -2…

A: Given , -x+y2=8, x=-2y, y=-2, revolved about x=-10. Find the volume of the solid generated by the…

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: The region bounded by y = x', y = 0, and x = 2 is revolved about the line x= 2. Find the volume of…

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Q: Find the volume of the solid generated by revolving the area bounded by x² – 2kx – 3ky + k² = 0 and…

A: Given curves are:  x2-2kx-3ky+k2=0 3x-3y+k=0 The area bounded by them is revolving about the line…

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: 7. Find the volume of the solid under the surface 1 = 3x+ 2y? above 1 < x < 3, 0 < y < 6 using a…

A: Introduction: We know that the volume under the curve z=f(x,y) and over the region R is given by the…

Q: Find the volume of the solid bounded by y=x2+1y=x2+1 and the line y=−x+3y=−x+3, revolved about the…

A: Given curves are y=x2+1 and y=-x+3 and the line y=5 Find the volume

Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky+k² = 0 and…

A: To compute the volume of the solid region enclosed by the curves y=fx and y=gx, where a≤x≤b and…

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 wedge cut from the first octant by the cylinder x2 + y2 = 1 and the plane 2x…

A: To find the limits of x, y and z from the region of integration, substitute 0 for y.…

Q: Find the volume generated by revolving the area bounded by y² – 4y – 4x + 4 = 0 and x 1 %3| about…

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Q: The volume of the solid obtained by rotating the region enclosed by y = x², y = 4x, about the line y…

A: We have to find the volume of the region.

Q: Find the volume of the solid bounded by x+y2=3z and x2+y2=6x.

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Q: What is the volume of the solid of revolution generated by rotating the area bounded by y%3D2, y3 3,…

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Q: first

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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…

Q: Find the volume of the solid bounded by the cylinders x2 + y2 = 4r2, y2 + z2 = 4r2.

A: We know that : Volume under the surface z = f(x, y) and above the region D in x-y plane is given by