Find the surface area of the portion of the sphere x^2 + y^2 + z ^2 = 1 that lies abovethe cone z =sqrt(x^2 + y^2) with x ≤ 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: 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: Find the volume of the solid generated of the area bounded by y = x², y + 2x = 8 and y = 0, rotated…

A: This question can be solved by first plotting the graphs to get the feel of the area enclosed.

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 bounded by the plane 2x + 8y + 5z = 2 in the first octant. Leave your…

A: Equation of plane, 2x + 8y + 5z =2

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 volume of the wedge cut from the cylinder x2+y2=25 and from the z=3y and z=0 planes,…

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Q: Find the area of the surface generated by revolving the region bounded by, y6 1 x = + 16y4 i 1<ys 5…

A: In this question, we find the surface area generated by rotating the region bound by the given curve…

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

A: See below for the solution.

Q: Find the volume of the solid bounded by the plane 3x + 8y + 4z = 10 in the first octant. Leave your…

A: In the given problem the first octant denotes the region in the coordinated plane where x,y,z≥0 The…

Q: Find the volume of the solid of revolution formed when the area of the region bounded by y3Dx2,…

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Q: What is the volume of the solid that is generated by revolving the region bounded by the curve y=…

A: Given curve is, y = 2x - x2 the volume of solid formed by revolving the region bounded by the curve…

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: Determine the right circular cone of maximum volume that can be inscribed inside a given sphere of…

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Q: A right circular cone is circumscribed by a sphere of radius 1. Determine the height h and radius r…

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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 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 volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Find the dimensions of the right circular cone of the greatest lateral area that can be inscribed in…

A: Here we find the dimensions of cone.

Q: y = 9x² and y = 0 about x = −4

A: Given:        y=9-x2 and y=0         x2=9           x=3 about x=-4

Q: ut the line x = 3.

A: The parabola equation is given , x2 = 4y. The equation of line is given , x = 4 - 2y. The volume…

Q: Determine the volume of the solid that will be generated by revolving the area bounded by the given…

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Q: Find the area of the surface generated by revolving the region bounded by, 1 1sx55 8x2 about the y-…

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

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Q: 4. Find the radius of the right circular cone with least volume that can be circumscribed about the…

A: Formula Used: Volume of Cone = 13πR2h where R,h denote the radius and height of right circular…

Q: Find the volume of the solid generated of the area bounded by y 8x and y 2x, rotated about %3D y =…

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Q: Find the volume of the solid cut from the first octant by the surface z=4-x2-y.

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Q: Find the dimensions of the right circular cone of the greatest lateral area that can be inscribed in…

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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: The altitude of a cylinder of maximum volume that can be inscribed in a right circular cone of…

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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: 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 whose base is the region enclosed between the curve x = 1−y² and the…

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Q: Find the volume of the solid generated of the area bounded by y = x², y + 2x = 8 and y = 0, rotat…

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Q: 9. Find the demensions of the right circular cylinder of largest volume that can be inscribed in a…

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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 solid generated when the regions enclosed between the curves y=x^2 and x=y^2 is…

A: Given curves, y=x2andx=y2 To find the volume of solid generated by these curves about x - axis.

Q: Find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius…

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Q: Find the volume of the solid generated by revolving the region bounded by the parabola y = 2x2 and…

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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: plane

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Q: Find the volume of the solid bounded by the plane 7x + 3y + 4z = 3 in the first octant. Leave your…

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Q: Right circular cones of height h and radius r are attached to each end of a right circular cylinder…

A: Let Vcr be the volume of the cone and Vc be the volume of the cylinder. So, Vcr=πr2h and Vc=13πr2h.

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

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Q: Find the volume and the surface area that generated due to rotate the bounded area between the curve…

A: I use washer method to find volume about x axis

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

A: We have given the curves; 2x+y=2 and y=2x+x2-x3 Which generates the cone revolving about the y-axis.

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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