to find the surface area cut from the sphere x^2+y^2+z^2=16 by the cylinder x^2+y^2-4y=0

Q: Find the volume of the 'cover' that is bounded by 52 < x2 + y2 + z² < 7² and the upper cone z² = 4x2…

A: Given 52≤x2+y2+z2≤72 ,z2=4x2+4y2

Q: Find the area of the surface generated by revolving x= 4/9 - y,0sys about the y-axis. 16 x=49-v 12

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Q: Find the volume of the solid that is bounded by the surfaces z = 82 - x2 - y2, z = 0, x = 0, y = 0…

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Q: Determine the dimensions of the right circular cylinder of maximum lateral surface area that can be…

A: Maximum lateral surface area will occur at critical point  So put ds/d(theta) = 0 Find theta

Q: Calculate the coordinates of the center of mass of the body delimited by the surfaces z = 9 - √x2 +…

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Q: Find the dimensions of the right circular cone of minimum volume V that can be circumscribed about a…

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Q: Find the volume of the solid that is bounded by the surfaces z = 192 - x2 - y², z = 0, x = 0, y = 0…

A: Find the volume of the solid.

Q: Find the volume of the solid generated when the region bounded by x = 2y², y-axis, the lines y = 3…

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Q: Show that a closed right circular cylinder of given surface has maximum volume if its height equals…

A: Let, the surface area be S, radius be r, height be h and volume be V. The total surface area be…

Q: Calculate the area of the surface bounded by y = x^3 and y = −2x^2 + 3x

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Q: please describe clearly, and type by computer  Describe how to set up a surface integral given that…

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Q: Find the volume of the region under the surface z = 6x° and above the triangle in the xy-plane with…

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Q: A right circular cylinder is inscribed in a sphere of radius r. Find the largest possiblesurface…

A: Consider the right circular cylinder inscribed in the sphere with radius, r. Suppose the height and…

Q: Explain why the explicit description for a cylinder x2 + y2 = a2 cannot be used for a surface…

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Q: Find the volume of the region under the surface z and above the triangle in the xy-plane with 1+ x²…

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

Q: What is the area of the enclosed surface bounded by the x-axis, x = 2 and y=x2 ?

A: The area under the curve can be calculated by the integration. The formula for the integration is…

Q: find volume of solid 3x^2 ,x=1, y=0 about x axis

A: Consider the region bounded by the curves y=3x2,x=1,y=0 as shown in the figure below: Here, the…

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Find the centroid of the area bounded by the y= 4x-x^2 and x+y=4. PLEASE PROVIDE A NEAT SOLUTION…

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Q: A right circular cone is generated by revolving the region bounded by y = 5x/12, y = 5, and x = 0…

A: 1. Lateral surface area of the right circular cone = pi*r*L     where pi = 22/7; r = radius of the…

Q: What is the surface area generated by revolving the parabola y = x squred from x = 0 to x = square…

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Q: Find the volume of the region under the surface z = 4x* and above the triangle in the xy-plane with…

A: The solution follows as

Q: (c) Semicircles (d) Isosceles right triangles y 2)

A: Part C) To find the volume of the solid whose bases are bounded by the circle x2+y2=4,  And the…

Q: 3. Show that a closed right circular cylinder of given surface has maximum volume if its height…

A: Let r, h be the radius and height of the cylinder respectively and V, S be the Volume and Surface…

Q: Determine the area of the surface generated by revolving y=x³ on (0,1), about the x-axis.

A: The given curve is y=x3  on 0, 1 about x-axis. This implies that,…

Q: Find the exact area of surface obtained by rotating the curve about the x-axis. y=sqrt(5-x)    3<…

A: Given curve is y=5-xdydx=-125-x Now, area of the surface obtained by revolving y=f(x) from x=a to…

Q: Use cylindrical coordinates to calculate the volume between the surfaces in the first octant if z =…

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Q: 3. Explain how we know that it is possible to cut a surface with continuous boundaries in exactly…

A: We should mathematically establish the possibility of cutting a surface with continuous boundaries…

Q: Find the maximum and minimum values of x^2 + y^2 − 2x − 2y on the disk of radius √ 8 centered at the…

A: Given function is  fx,y=x2+y2-2x-2y where bounded region is  x2+y2≤8.

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 surface area generated by y = x³; x = 0 and x = 3 and is revolved on x-axis.

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Q: The base of a solid is the region bounded by the line y = 9 and the parabola y = x². Cuts…

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Q: Find the volume of the solid which lies under the graph of z = x2 + 6y2 and over the triangular…

A: The Volume is=∫∫D ℤ dxdy where D is the region in the xy plane having vertices0,0,0 , 1,0,0 and…

Q: Find the area of ​​region R bounded by y = 2x, y = 5x and y = 5 in the first quadrant  NOTE: The R…

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Q: Calculate the volume of the region bounded by the spherex + y² + z² = 9 from above and by the cone…

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Q: Calculate the surface area of the surface given by z=x^2+y^2 over the region 0<x<2 and 0<y<min(x,…

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Q: Find the volume of the solid that lies under the plane 4x+6y-2z+15=0 and above the rectangle…

A: Consider the given plane

Q: find the areas of the surfaces generated by revolving the curves about the given axes. 27. x = 24y -…

A: To determine the surface area of solid of revolution about the y-axis.

Q: Find the volume of the largest right circular cone that can be incribed in a sphere of radius 3. 3 y…

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Q: Find the volume of the region cut from the solid cylinder x^2 + y^2 less or equal to 1 by the sphere…

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Q: Explain how to set up a surface integral given that you will project the surface onto the xz-plane.

A: Let the provided surface is S and the function is f whose integral over surface S is to be find.…

Q: Calculate

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Q: Find the exact area of surface obtained by rotating the curve about the x-axis. y=sqrt5-x   3< x <…

A: consider the equation

Q: Find the volume of the region above the triangle with vertices (1,0), (0,1) and (3,1), below the…

A: Given Data: fx,y=x2y The vertices of the triangles are (1,0), (0,1) and (3,1).

Q: If the line x = 1- y, with 0 < y<1 is revolved about the y-axis. Find the generated lateral surface…

A: Given  the line x = 1-y with 0≤y≤1 is resolving about the y-axis we have to find the generated…

Q: Assume we wish to to make a right cylindrical can with a bottom and no top, and with a capacity of…

A: Solve it

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 under the surface z = 9x and above the triangle in the xy-plane with…

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Q: An oil storage tank can be described as the volume generated by revolving the area bounded by…

A: Given: y=49+x214, x=0, y=0, x=2 To determine: The volume of the tank generated by revolving the area…

Q: Find the area of the surface generated by revolving the region bounded by, 1 + 6 y 1<x < 3 16x4…

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