Find the area of the portion of the unit sphere inside the cylinder x2 + y? = 1/2 and z > 0. Select one: a. 3(2 - V2)T b. 2(2 - V2)T С. 4(2 – /2)n d. Non of them е. (2 – V2)T

Q: given ∫∫s (x2z) dS and S is the part in z = sqrt(x2+y2), which lies in x2+y2 = 1 calculate the…

A: we have to evaluate ∬Sx2zdS Now, we have z=x2+y2 ⇒z2=x2+y2∂z∂x=xz and…

Q: Find the volume of the solid generated by revolving the shaded region abouti хаxis Q 3x+ 5y = 15 5

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Q: The triangular plate in the first quadrant bounded by y = x, x 0, and y = 2-x with p(x,y)= 16x + 5y…

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Q: Find the volume of the solid above the cone z2= 3(x2 + y2 ), z ≥ 0 and below the sphere x2+ y2+ z2 =…

A: We convert the units in spherical coordinate. The cone is given as,  The sphere is given as, The…

Q: Find the surface area of the portion S of the cone z^2=x^2+y^2 where z≥0z≥0, contained within the…

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Q: Use the disk method to verify that the volume of a sphere is 4/3 πr3 , where r is the radius ?

A: So sphere is basically a circle that is rotated through the x-axis. We will suppose to cut a disk…

Q: 4. Find the volume of the solid generated by revolving the first quadrant area of the curves xy=2,…

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Q: A right circular closed cylinder with radius r cm and height h cm is placed on a square block with…

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Q: A metal sphere weighing 24 kg is melted down and recast into a solid cone of base radius 8.0 cm. If…

A: Given that , Mass of metal , m=24 kgDensity of metal , ρ= 8000 Kgm3Radius of Cone , r=8 cm…

Q: Find the volume of the region cut from the solid sphere (x2 + y2 + z2 < 4a2) by the cylinder 40 (x²…

A: Given x2+y2+z2≤4a2x2+y2=a2

Q: Find the volume of the smaller wedge cut from a sphere of radius 10 by two planes that intersect…

A: Here we have to find the volume of the similar wedge cut from a sphere of radius 10 by two planes…

Q: 5. Find the volume of spherical wedge formed by rotating through an angle of 45 a semi circle of…

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Q: 3. Find the surface area of the object obtained by rotating y = 4 + 3x?, 1<x<2 about the y-axis.

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Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is

A: Given

Q: Find the volume of the solid cut from the cylinder x2 + y? = 25 by the planes z = 0 and x + z = 2.

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Q: Find the area of the portion of the sphere of radius 4 (centered at the origin) that is in the cone…

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Q: The volume of the solid region, in the first octant, that lies below below the surface, z = above…

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Q: Q3: Find the volume of the solid enclosed by the parabola y = x² +z? and the cone y = 32 – x² - z2.

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Q: Consider a right circular cylinder open top tin can with volume 1000 cm3. Suppose R and H are the…

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Q: a. The volume of the solid generated by revolving the region bounded by y= 4yx and the lines y =…

A: Given that, y=4x,y=414 and x=0. Obtain the limit of the region. 4x=414 x=14 x=14 Sketch the region…

Q: (c) By using double integrals, find the surface area of plane 2x + 5y + z = 10 that lies inside the…

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Q: 3. Find the volume of a solid enclosed by the parabolic cylinder y = x², the planes z = 0 and y +z =…

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Q: Find the volume of the solid cut from the cylinder x² + y? = 4 by the planes z = 0 and x +z = 6.

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Q: Find the surface area of the planez= x +y?from z=4 to z=9?

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Q: Find the volume of the solid that lies within the sphere x² + y + z² = 81, above the xy plane, and…

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Q: Find the radius ? and height ℎ of a cylindrical can of total surface area 110 cm2 whose volume is as…

A: NOTE: Refresh your page if you can't see any equations. . the surface area of the cylinder is given…

Q: An oil storage tank can be described as the volume generated by revolving the area bounded by 4 Y =…

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Q: Find the volume of the solid enclosed by the paraboloids z = 16 (x² + y²) and z = 8 − 16 (x² + y²).

A: We have to find the volume of the solid enclosed by the paraboloids z=16(x2 +y2) and z=8−16(x2 +y2).…

Q: 5 Find the lateral (side) surface area of the cone generated by revolving the line segment y =7x,…

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Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 3 and the upper cone z? = 4x2 +…

A: Let's find.

Q: The base of solid is given by 9x² +4y = 36 on the xy-plane. The cross section is a square that is…

A: Let A(x) denote the cross-section area in a plane perpendicular to the x-axis, where a≤x≤b. Then,…

Q: * Q. (41), p.305 : Find the volume of the solid generated of revolving V3 1 y V1 + x2 SxS V3 3 < x s…

A: The volume of a solid obtained by revolving the curve   about the x-axis from to is given by the…

Q: Find the volume of the solid bounded below by the circular cone z = 3.51/x² + y and above by the…

A: To calculate the volume of the solid bounded below by the cone z=3.5x2+y2 and above by the sphere…

Q: A circular swimming pool full of water has a diameter of 24 ft and the sides are 5 ft high. Set-up…

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Q: Vx² +y² and A metal plug has been designed using the intersection of the two cones z = x² + y2 += 1.…

A: We have to calculate volume of plug which is intersection of two cones z=√(x2+y2) and z/3+√(x2+y2)=1…

Q: Maximize the lateral surface area of an inverted cone, if V = 100 cm³. S trvr² + h? V = 1h = 100 t…

A: According to company rule we can answer only first question and rest can be reposted.

Q: 3) Find the volume of the sphere: 4. V =r 3x5y6

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Q: The curre y=J36 - z' , -4£ x s4 will be rotated about the ルーaXis. find the area that results af the…

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Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 20 + x² - y? and above…

A: We have given z = 20 + x2 − y2 and R = [−2, 2] × [0, 4]

Q: A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with a liquid of weight…

A: Solution

Q: Find the volume of the solid enclosed by the paraboloids: z = 2x² + y? and z = 27 – x2 – 2y². %3D |

A: The given equation of the paraboloids are: z=2x2+y2 and z=27-x2-2y2 Find the volume of the solid…

Q: Maximize the lateral surface area of an inverted cone, if V = 100 cm3. = TrVr² + h? V = 1h = 100 S…

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Q: 9. Find the surface area of the part of the cylinder y? + z2 = 9 that is above the rectangle R =…

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Q: Use the method of disks to rotate a circle of radius r around the x axis and prove that a sphere of…

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Q: 135 Find the area of the surface generated by revolving x = 4V9 - y. 0sys- about the y-axis. 16

A: Solution

Q: Find the total length of the cable. L = 2y + 3√² +6² + constant Differentiate both sides.

A: the solution next step..

Q: Determine the solution in finding the dimensions of the right circular cylinder, with the greatest…

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Q: Find the volume of liquid needed to fill a sphere of radius R to height R y V = 씨5

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Q: Use the disk method to verify that the volume of a sphere is (4/3)π r3 , where r is the radius.

A: Volume of sphere of radius r is (4/3) πr3

Q: 2r In cylindrical coordinates, the integral rdzdr d0 represents the volume of a solid... in between…

A: We will find out the required solution.