61. Show that the solid (an ellipsoid) obtained by rotating the region R in Figure 15 about the y-axis has volume nab. FIGURE 15 The ellipse (E)+G)´ = 1.

Q: 5. Find the volume of the solid generated by revolving the area of a circle: (x - 2)² + y² = 4;…

A: In this question, we need to find the volume of solid generated by revolving the area of the given…

Q: 10. Show that the volume inside the ellipsoid ++=1 is 4abe (Hint: Use the change of variables x =au,…

A: We have to find volume of ellipsoid: Concept:

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above…

A: The volume of the enclosed region under the, hyperbolic paraboloid z = f(x,y) and above the…

Q: A solid dome is to be constructed with the ellipse x^2+3y^2=6 as a base. Using infinitely many…

A: Given that the solid dome is to be constructed with the ellipse x2+3y2=6 as a base. We have to…

Q: a) Find the volume and the lateral surface area of the solid formed by rotating this func- tion…

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Q: 2 Find the volume of the region between the ellipsoid (=) = 1 and the plane 4 8. - | א + నా | co

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Q: 4. Find the volume generated by revolving the area cut off from the parabola y = 4x - x² by the x…

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Q: 9–6. Locate the centroid ỹ of the area. 1 m -2 m

A: We need to find the y-coordinate of centroid of the region given. if we have the region bounded by…

Q: Find the volume of the ellipsoid =D1 in positive octant Once

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Q: The volume of the solid generated by revolving the region between the parabola x =y²+1 and the line…

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Q: = Find the volume of the ellipsoid x² + y² + 6z² 64.

A: Given,                x2+y2+6z2=64.

Q: (1 point) The volume of the solid obtained by rotating the region enclosed by y = a², y = 2x, about…

A: y=x2y=2x about line x=2 for point of intersection x2=2xx2-2x=0x(x-2)=0x=0,2

Q: Find the volume of the shaped body bounded by the z = 3x2 + 3y2 and          z = 4 - x2 - y2…

A: We have to Find the volume of the shaped body bounded by the z = 3x2 + 3y2 and        z = 4 - x2 -…

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 2 and above…

A: Given:z=3y2-x2+2 above the rectangle R=-1,1×1,5Formula:V=∬R z dx dy

Q: find the volume of the solid obtained by rotating region B in Figure 13 about the givenaxis. x-axis

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Q: Find the volume of the solid enclosed by the coordinate plane and the plane 2x + 3y + 6z = 6 using…

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Q: 2. Suppose you revolved the triangular region bound by the axes and the line 4x + 3y = 12 completely…

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Q: Find the volume of the solid formed by revolving the area bounded by the parabola y2 = 9x and the…

A: We want to find the area bounded by the parabola y2 = 9x and the line y = 3x about the y-axis.

Q: 1) Compute the volume of the solid obtained by revolving around the r-axis by 27 (ie. a full…

A: Note: Since, you have asked multiple question, we will solve the first question for you. If you want…

Q: 24 22. Find the volume generated by revolving about Ox the area bounded by the Ans. ra³. hyperbola…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 2.4. Find the volume of the solid generated by revolving the region bounded by y = 5a about the…

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Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

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Q: Suppose top part of the ellipse (x^2/a^2) + (y^2/b^2) = 1 is rotated about the x-axis. Find the…

A: We want to find volume of the solid we obtained by revolving about x axis.

Q: Consider the region in the first quadrant and further bounded by the graphs of y = arcsec x, y=1,…

A: Consider the region in the first quadrant and further bounded by the graphs of y=arcsec(x),  y=1,…

Q: The “triangular” region in the first quadrant bounded by the x-axis, the line x = 4, and the…

A: Given,

Q: 1. The region in the first octant between two spheres centered at the origin; one of radius 2 and…

A: Given the density function and region

Q: What is the volume of the solid whose base is the interior of the parabola y2 = x from x=0 to x=4…

A: Given parabola equation is  y2=xTake square root on both sidesy=x Now we find area of square shaped…

Q: 2 Find the volume of the ellipsoid 2y 7z 16

A: Volume of the ellipsoid for the equation,

Q: find the volume of the solid obtained by rotating region B in Figure 13 about the givenaxis. y = 6

A:

Q: Find the dimensions of a right cone with surface area S=4 n that has the largest volume?

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4. Determine the surface area of the solid obtained by rotating y = v9 – x2, -2 < x<2 about the x -…

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Q: 4. Find the volume of the solid generated by revolving the region between the y – axis and the curve…

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Q: 2. Find the volume of the solid generated when the region enclosed by the curve y = x² + 1, y = 4x −…

A: To find the volume of the solid generated when the region enclosed by the curves  y=x2+1 , y=4x-x2+1…

Q: What is the volume of the solid whose base is the interior of the parabola y2 = x from x=0 to x=4…

A: Volume of the solid obtained by revolving y=f(x) between x=x1 and x=x2 about x-axis  is,…

Q: Between the parabola y = -x² + 4x – 3 and the line y = x – 3 Find the volume of the solid formed by…

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Q: Consider the plane region bounded by the graph of the ellipse (x/a)2+( y/b)2 = 1 where a &gt; 0 and…

A: Given: To Find: (a). The volume of the ellipsoid formed when the region is revolved around the…

Q: Find the volume of the ellipsoid x² + y² + 10z² = 49.

A:

Q: Consider the region enclosed by graphs of y = x^2, x = 0, and y = 9. Find the exact volume of the…

A:

Q: find the volume of the solid obtained by rotating region A in Figure 13 about the givenaxis. y = 2

A:

Q: find the volume of the solid obtained by rotating region B in Figure 13 about the givenaxis. x = 2

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Q: 1. Find the volume of the solid that results when the shaded region is revolved around the Y - AXIS.…

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Q: What is the volume, in cubic units, of the rotating body formed by rotating the region bounded by…

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Q: find the volume of the solid obtained by rotating region A in Figure 13 about the givenaxis. x-axis

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Q: 5. Find the volume of the solid generated by revolving about the x-axis the smaller area bounded by…

A: Solution :- As per guidelines . I do first only.

Q: Find the volume of the solid generated by revolving the shaded egion about the y-axis. x- 4 tan y 4

A: Topic:- application of integration