Find the surface area of the torus obtained by rotating the circle x2 + (y – b)? =r² about the x-axis (Figure 20). (0, b+ r) (0, b) FIGURE 20 Torus obtained by rotating a circle about the x-axis.

Q: Find the area of the surface generated by revolving the curve y = sqrt(x + 1) , 1 <= x <= 5 about…

A: Given that the surface is generated by revolving the curve y=x+1 , 1 &lt;= x &lt;= 5 about the x -…

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 torus obtained by rotating the circlex 2 + (y - b )2 = r 2 about the…

A: Given the equation of the circle  x2+(y-b)2=r2. We need to find the surface area of the torus…

Q: 10. у %3D /5 — х, 3 <x < 5

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Q: Find the area of the surface generated by revolving the curve y = Vx + 3, 4 < y <7 around the…

A: We have to find area of the surface . Given y=x3+3                                 4≤y≤7

Q: B- Find the area of the surface generated by revolving the curve y = √√2-x² about x-axis

A: Introduction:   An object's surface area is the total area that all of its surfaces occupy. The…

Q: Q2 Calculate 8- z dz, z(4- z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Find the area of the surface generated by revolving the curve y = sqrt(x2 + 2), 0…

A: find dy/dx and solve for ds.

Q: Compute the surface area of the portion of the hyperboloid x² + y? -? = 64 between z = 7 and z = 8.

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Q: Q2 Calculate 8- z dz, z(4-z)* where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Find the area of the surface generated by revolving x =t+ 2/5, y= +2/5t, -2/5 sts2/5 about the…

A: Here we will find out area of surface of revolution.

Q: find the the area of the surface obtained by rotating the circle about the line x^2+ y^2=25…

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Q: Find the exact area of the surface obtained by rotating the curve about the y- axis: y = 3 + 5x?,…

A: Consider the given function and interval. y=3+5x2, 3≤x≤8 If y=f(x) is function and the interval of y…

Q: Determine the area of the surface generated by rotating around the "y" axis, the curve described by:

A: Here, the given parametric curve is: x=t33, y=t+1; 1≤t≤2⇒x'(t)=t2, y'(1)=1 Now, the surface area…

Q: Surface at θ = 40⁰ and r = 20 is a     plane    cirlce   cone

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Q: Find the area of the surface generated by revolving the curve

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = sqrt(7-x),…

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Q: Find the area of the surface generated by revolving the curve y = √(x2 + 2), 0 ≤x ≤ √2, about the…

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Q: The figure shows the surface created when the cylinder y2 + z2 =1 intersects the cylinder x2 + z2 =…

A: It is given that, the cylinder y2 + z2 =1............... (1) intersects the cylinder x2 + z2 = 1…

Q: Which one, y=ex, 1≤y≤2, gives the surface area of the solid formed by rotating the curve segment…

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Q: The lateral (side) surface area of a cone of height h and base radius r should be Ar v? +h?, the…

A: Consider the provided question, Given the line segment, y=rhx,  0⩽x⩽h Differentiate both side of…

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is Then x…

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

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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 generated by revolving the curve y=−x^3/18​, −2√2≤x≤0​, about the​…

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Q: Find the surface area of the cone frustum generated by revolving the line segment y = 4 1 over 1 < x…

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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: 4. Find the area of the surface generated by revolving the curve y = v9 – x², - 2 < x < 2, about the…

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Q: Evaluate the exact area of the surface obtained by rotating the circle x2 + y² = r² about the line y…

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Q: Find the area of the region in the second quadrant that lies between the circle r = π and the spiral…

A: Second quadrant is  [pi/2 ,pi]

Q: Find the area of the surface generated by revolving the curve Y = 8/x, 2 < x < 7 around the -axis.

A: The given surface is generated by y=8x,  2≤x≤7 around the x axis. The area of the surface generated…

Q: 7. Find the surface area of the cone frustum generated by revolving the line segment x 1 y ==+ 1s…

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Q: Find the area of one side of the “winding wall” standing orthogo-nally on the curve y = x2, 0 &lt;=x…

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Q: Calculate the area of the surface of rotation created by rotating the curved segment about the…

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Q: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

Q: 9. y = x', 0< x< 2

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Q: メ y= oL Xとn2

A: Given curve is y=ex , 0≤x≤ln2find the area of the surface

Q: The area of the surface obtained by rotating the curve y = V9-x2, -3 < x < 3 about the x-axis is

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Q: Find the area of surface that is generated by revolving the portion of the curve x = /9 – y? , -2 <…

A: We will find out the surface area of revolution.

Q: find the surface area obtained by rotating the circle (x – 4)2 + y? =1 about the y-axis. %3D

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Q: Find the exact surface area for the portion of the surface z=sqrt(x^2 + y^2) that is below z=4 and…

A: Find the exact surface area of the portion of the surfacez=x2+y2 that is below z=4 and in the region…

Q: The lateral (side) surface area of a cone of height h and base radius r should be pai rsqrt(r2 +…

A: Obtain the lateral surface area as follows.

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 2t, y = 3t,…

A: TO FIND THE AREA GENERATED BY THE REVOLVING BELOW SURFACES x =2t y =3t ,   0≤t≤9 FORMULAS USED (a)…

Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

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Q: y = x, 0 < x <7

A: The given line  y = (7/5)x This is revolved about x axis  0≤x≤7

Q: Find the area of the surface obtained by rotating the curve y2 = 4x + 4 0<x<8 about the x-axis? %3D

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Q: Find the exact area of the surface generated by revolving the curve about the stated axis. y = Vx…

A: The formula for area of surface generated by the revolution of curve y=f(x) , a≤x≤b about x-axis.…

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 exact area of the surface obtained by rotating the curve abo = V7 - x, 1<x< 7

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 6t, y = 9t,…

A: Here,  we need to find the surface generated by revolving the curve x=6t, y=9t, 0≤t≤3, about each…