y e 3x, x 2 0, is rotated about the x-axis, find the area of the resulting surface. If the infinite curve Find the surface area of the torus shown below, with radii r and R. R

Q: 29. The shaded band shown here is cut from a sphere of radius R by parallel planes A units apart.…

A: To show: That the surface area of the band is 2πRh. Given: The shaded band is cut from a surface pf…

Q: b) The curve y = }(r² – 2 In r), 1<r< 4, is rotated about the y-axis. Find the area of the resulting…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 4x = y? + 20,…

A:

Q: 1. Find the surface area generated by rotating the portion of the parabolic are y = x² from x = 0…

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Q: For an ellipse which every point represented by i = a cose î + bsin0 ĵ , calculate the area using $r…

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Q: The point P, on the surface z? = (x – 27)y + 1, is the closest point to the origin. Find the…

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Q: 3/ Math

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Q: The line segment joining the points (0, 1) and (2, 2) is revolved about the x-axis to generate a…

A: To determine the surface area of the frustum.

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = Vx, 1sy& 4

A:

Q: Find the surface area generated by rotating the parabola arc y = x² about the x-axis from x = 0 to x…

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Q: Identify the surface p = cos p. Select one: O a. sphere of radius 1 O b. cone O c. * sphere of…

A: The given equation is, ρ=cosϕ. Multiply both sides of the equation by ρ. That is, ρ2=ρcosϕ. It is…

Q: Find the points on the surface y? = 36 + xz that are closest to the origin. smaller y-value (х, у,…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = Vx, 3sy54

A: Given:y=x3  ,     3≤y≤4Surface area :S=∫ba2πx 1+dxdy2   dy

Q: Find the area of the surface generated by revolving the curve about the indicated axis. y = x3/9, 0…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. x3/2, 0sxs 21 y

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Q: for the Surface Area below ... what is the * ?radius of revolution The area of the surface obtained…

A: The radius of the revolution is the distance between the centroid of the curve and the axis of the…

Q: Describe and provide a rough sketch of the surface determined by the following equation: -x² +4y? -…

A:

Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

Q: Consider the surface defined by the equation 2.x2 – 2y2 – z = 0. (a) Choose any one of the variables…

A: The equation is the form z=f(x,y) represents a surface in the space. In this problem the equation of…

Q: Let S be the surface of the portion of the cone z? = x² + y² that is contained in the cylinder r? +…

A: According to the given information, let S be the surface of the portion of the cone that is…

Q: Find the surface area obtained by revolving the parabola x? = 4y from x = 0 to x = 2 about the…

A: If a curve f(y) is revolving about the y-axis over the interval [a,b], then the surface area is:…

Q: Find the area of the following surface using a parametric description of the surface.   The cap of…

A: Consider the surface that is the cap of sphere:

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = x2 - 1 -…

A:

Q: Find the points on the surface y? = 81+ xz that are closest to the origin.

A: Distance formula is                   d2=x2+y2+z2                  d2=f=x2+81+xz+z2 Since,…

Q: Find the surface area of the cone frustum generated by revolv-ing the line segment y = (x/2) +…

A: Consider the given line segment,The surface are of the cone frustum generated by revolving the line…

Q: Calculate the surface area of the following: (a) the cap cut from the sphere x² + y? + z2 = 3 by the…

A: We need to find the surface area of the portion of the sphere x^2+y^2+z^2 =3 above z=√x^2+y^2

Q: dV , where V is the unit sphere.

A:

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

A: Given : surface S (say) is created when the cylinder y2+z2=1 intersects the cylinder x2+z2=1 To find…

Q: The tangent plane to the graph of the surface z=in(x2+y?} at the point (1,0,0) contains point…

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Q: 4. Find the area of the surface obtained by rotating the curve y? = x + 1, 0<x < 3. about the x-axis…

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Q: The area of an ellipse is rab, where a and b are the lengths of the semimajor and semiminor axes.…

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Q: The given curve is rotated about the y-axis. Find the surface area of the resulting surface. 22/3 +…

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Q: Find the area of the surface generated by revolving the parabolic arc y = x 2 for 0≤x≤ 1 about the…

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Q: Find the surface in the accompanying area of the heli r(r,0) = (rcos0)i+(r sin 0) j + Ok, 0s0<2r,…

A: Introduction: The formula for the surface area of the function r(r,θ) is given by,…

Q: H The cooling tower in a power plant is modeled as an open-ended body where the center of the…

A: Given: R=270 feet r=45 feet H=160 feet

Q: For each surface T(u, v), identify the best description of the surface's shape. F(u, v) Shape a.…

A: Any point on the three dimensional surface can be represented as x, y, z. The equation between x, y,…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. 1 In(x), 4< x <…

A:

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = ? - Incx),…

A: Given that: y=14x2-12ln(x),     2≤x≤5

Q: Q. The curve y = v4 – x², -1 <x<1, is an arc of the circle x? + y? = 4. Find the area of the surface…

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Q: The given curve is rotated about the y-axis. Find thearea of the resulting surface.   x =  1/4 x2 -…

A: If the curve y = f(x) , a≤x≤b is rotated about y axis , then surface area is, A=2π∫abx1+f'x2d

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

A: The surface area formula using integration is given by: In the question, we are given: Also x lies…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. x = Va? - y²,…

A: We are given the equation of the surface as x=a2-y2, 0≤y≤a3. We need to find the area of the above…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = =x² - 1 1,2…

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Q: 2) | cos(r + y)dA, R is the unit disk (i.e. the region inside the unit circle)

A: This double integral can be easily solved in polar coordinates. A brief introduction to polar…

Q: For the conical surface 0 = 30°,0 <0< 21,0 <r< 2, the lateral surface area is what?

A: Sol

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = Vx, 2 < y<…

A: Given: The given curve is, y=x3=x1/3,  2≤x≤4   To determine: The area of the resulting surface.…

Q: The accompanying figure shows a spherical cap of height h cut from a sphere of radius r. Show that…

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Q: Find the surface area of the torus obtained by rotating the circle x2 + (y – b)? =r² about the…

A:

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x between x…

A: Given; y=x^2 between x=1 to x=2

Q: Name the surface and draw an accurate Graph of z = xʻ in R’.

A: