Find the surface area of the portion of the cone 22 = 4x² + 4y? nat is above the region in the first quadrant of the ry-plane that is ounded by the line y = 1 and the parabola y = x². .

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Find the area of the surface generated by generated by revolving the curve about the r-axis. と4u:4+…

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Q: Find the area of the surface generated by revolving x = t+2/3, y = +2/3t+3, -2/3 sts2/3 about the…

A: The surface area of disk is s=πr2 h  where r is radius and h is width

Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

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Q: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

Q: Find the area of the ellipse cut from the plane z = cx (c a constant) by the cylinder x2 + y2 = 1.

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Q: Find the surface area of the portion of the bowl z = 8+x² + y that lies below the plane z = 14.

A: Given, z=8+x2+y2 ,z=14 Now substitute z=14 into the given surface for finding the intersection of…

Q: Find the area of the surface. The part of the paraboloid z = 1 − x2 − y2 that lies above the plane…

A: Given that the part of the parabola z=1-x2 -y2 that lies above the plane z= -6 . Here we have to…

Q: Find the area of the surface obtained by rotating the curve x = /16 – y², 0 <y<2, about the y- axis.…

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Q: Find the area of the surface. The surface cut from the bottom of the paraboloid z = x2 + y2 by the…

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Q: The volume of the tetrahedron enclosed by the coordinate planes and the plane 9x +y +Z = 18 is ?

A: We want to find the volume of the tetrahedron enclosed by the co-ordinate planes, i.e. x=0, y=0, z=0…

Q: Find the area of the surface cut from the paraboloid x2 + y + z2 = 2 by the plane y = 0.

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Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder 22 + y?…

A: We have to find surface area of the plane z=5+4x+3y that lies inside the cylinder x^2+y^2=16.

Q: Find the area of the surfaces The surface cut from the bottom of the paraboloid z = x2 + y2 bythe…

A: The formula for the surfaces area of the paraboloid above the region R is: A=∬Rzx2+zy2+1dxdy Where,…

Q: Find the surface area of the portion of the surface x2- 2 In a+ V15 y - z = 0 above the rectangle 1…

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Q: . Find the area of the surface obtained by rotating y = S, Vs² – 1 ds, 1 < x < 2 about the y-axis.

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Q: Find the surface area of the portion of the cone z? = 4x? + 4y? that is above the region in the…

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Q: Find the area of the surface obtained by rotating the curve y 4V7,0 < I < 5, along the r-axis.

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Q: Find the area of the surface. The part of the paraboloid z = 1 – x² – y2 that lies above the plane z…

A: Givenz=1-x2-y2z=-2Suppose the surface is defined byz=f(x,y) for x∈R, then the area of the surface is…

Q: Find the area of the plane region that lies below the line y = 2x and between the parabolas y= 2x^2…

A: Given Curves are:…

Q: Find the area of the surface that is generated by revolving the portion of the curve y = 2/1-, zE…

A: Use formula of surface area revolved about x axis

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Find the area of the portion of the plane 3x − 3y + z = 12 that lies inside the cylinder y^2 + z^2 =…

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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Q: Find the surface area of the part of the plane 7+ 2x + 5y that lies above the rectangle [1, 4] x [0,…

A: Given that  Z=7+2x+5y To find the area of the surface of the plane that lies above the rectangle

Q: Find the area of the surface generated by revolving x = t+2/3, y =+2/3t+1, -2/3 sts2/3 about the…

A: Find the area of the surface generated by revolving the graph of the following parametric equation…

Q: Find the area of the surface. The portion of the plane y + z = 4 that lies above the region cut from…

A: Given:

Q: Find the area of the ellipse cut from the plane z= 8x by the cylinder x +y = 4. Surface area = (Type…

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Q: Find the surface area for the portion of the hemisphere z =sqrt(4 − x^2 − y^2) that sits above the…

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Q: Find the surface area of the part of the plane 3x + 2y + 4z = 24 that lies in the first octant…

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Q: Compute the surface area of the ellipse that lies on the plane z = 11 – 3x + 2y and inside the…

A: The surface area of the surface given by z=f(x,y) where (x,y) is a point from the region D in the…

Q: How many square units is the area of the surface obtained by rotating the curve y = V4-z, 0 <I<2…

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Q: Find the area of the surface cut from the paraboloid x2 + y2 - z = 0 by the plane z = 2.

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Q: Find the surface area of that part of the plane 6x + 8y + z = 7 that lies inside the elliptic…

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Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

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Q: Calculate the surface area of the paraboloid with top radius R> 0 defined by 2 a² + y? 0< x² + y? <…

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Q: Find the surface area of the plane 3x + 2 y + z = 6 that lies in the first octant.

A: The surface area of the plane z=f(x,y) is given by the formula                          S=∬D…

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: Show that the volume of the segment cut from the paraboloid x2 /a2 + y2/ b2 = z/ c by the plane z =…

A: Show that the volume of the segment cut from the paraboloidX^2 /a^2 + y^2/ b^2 = z/ cby the plane z…

Q: Find the area of the surface. The part of the plane 3x + 2y + z = 6 that lies inside the cylinder…

A: Find the area of the surface. The part of the plane 3x + 2y + z = 6 that lies inside the cylinder…

Q: Find the area of the part of the sphere x+y +z = 16z that lies inside the paraboloid z =x²+y?.

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Q: Find the area of the portion of the surface x2 - 2z = 0 that lies above the triangle bounded by the…

A: Definition used:

Q: Find the area of the surface obtained by rotating the curve y=1/3 x3/2, 0≤y≤12  about the y- axis.

A: Let a rectangular strip parallel to x-axis of thickness dy be made whose tip touches the curve…

Q: Find the surface area of the part of the plane z = 7+ 5x + 3y that lies inside the cylinder 2+ y² =…

A: Surface area: -The definite double integrals determine the surface area of any surface enclosed by a…

Q: Find the area of the finite part of the paraboloid y = x² + z? cut off by the plane y = 16. [Hint:…

A: Surface area in xy-plane

Q: Find the area of the surface obtained by rotating thecircle x2 + y2 = r about the line y =r.

A: We have to find the area of the surface obtained by rotating the circle x2 + y2 = r about the line y…

Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…