Use triple itegral.in cylindrical. coordinates to mass of a- find. sphere .with density S. te. ass and raolius 2 ceutered at 12,0,0).

Q: Find the volume generated by the equation x? + y² – 4x – 6y – 12 = 0 if it is rotated about the line…

A: The volume of the solid generated by resolution can be calculated by calculating the surface area of…

Q: (a) Use the disk method to find the volume of the sphere x? + y? + z? = r. (b) Find the volume of…

A: (a).

Q: Calculate the moments M, and My and the center of mass (x, ỹ) of a lamina with the given density and…

A: The moments of the lamina can be calculated using the equation Mx=∬Ryρx,ydA and My=∬Rxρx,ydA. Now,…

Q: 25. Find the volume of the solid that is enclosed by the cone z = Vx² + y? and the sphere 22 + y? +…

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Q: Find the mass of the regien R which enclosed by the circle x qy2-1 and above the A -a xi's i s…

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Q: Use polar coordinates to find the volume of the given solid. Inside the sphere x² + y2 + z? = 16 and…

A: Given sphere is x2 + y2 + z2 = 16 and cylinder x2 + y2 = 1.

Q: wi the shope Find the mass of a spung of a conical helix řCt) = where ost 2T and s(xiy,2)= 2 gr/cm.

A: According to the given information, it is required to find the mass of a spring that is in the shape…

Q: Find, using spherical coordinates, the volume of the solid enclosed by the sphere x2 + y? + z2 = 9…

A: Here is the solution of the given problem. Volume bounded by the sphere and the plane z=2

Q: Using spherical coordinates, determine the volume of the solid that is above the z=2 v3 plane and…

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Q: In isosceles trapezoid WXYZ with bases ZY and WX, ZY = 8, YX = 10, and WX = 20. Find height h (the…

A: Given  The  WXYZ  is isosceles trapezoid  with bases ZY and WX .  Here ZY =8  , YX =10  and WX =20

Q: Find the moment or center of mass of the wire, as indicated. 10) Find the moment about the x-axis of…

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Q: b) Using Spherical Coordinates, find the volume of the solid G bounded above by the sphere x2 + y? +…

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Q: V=$t re h for r (geometry, volume of a spherical tuumor).

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Q: Determine the coordinates of the mass center of the welded assembly of uniform slender rods made…

A: Given data, Let ρ = density per unit length

Q: The circle x2 + y2 = a2 is rotated about the x-axis to generate a sphere. Find its volume.

A: we have been given that the circle x2 + y2 = a2 is rotated about the x-axis to generate a sphere. we…

Q: Using cylindrical coordinates, compute for the volume of A.

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

Q: Find the radius of the sphere x2 + y? + z? – 2x – 8 = 0. %3D 4 O 2 O 3 9,

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Q: Find the lateral surface area of the part of the cylinder a + y = 1 that lies within the sphere z²…

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Q: Use cylindrical or spherical coordinates, whichever seems more appropriate. Find the volume of the…

A: Given:A sphere of radius 10 by two planes that intersect along a diameter at an angle of π/2.

Q: Determine the diameter of a closed cylindrical tank having a volume of 11.3 m? to obtain a minimum…

A: Formula: Volume of cylinder: πr2h Surface are :2πrh +2πr2

Q: Consider the parallelepiped with adjacent edges Find the volume. V = i u = Si + 5j + k v = i + j +…

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Q: What is the volume of the following region, described in spherical coordinates? 1<p<9, 0 s

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Q: Use polar coordinates to find the volume of the given solid. Inside the sphere x2 + y2 + z? = 25 and…

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Q: Find the area of the portion of the unit sphere inside the cylinder x2 + y? = 1/2 and z > 0. Select…

A: The equation of the sphere is x2+y2+z2=r2. Here, r is the radius of the sphere. The equation of the…

Q: Find the volume of the solid that lies inside both the cylinder x + y = 1 and the sphere a? + y? +…

A: Volume between given two shapes can be calculated by the method of triple integration.

Q: Sdlid inside x²+y?+2²=16outside

A:

Q: In isosceles trapezoid WXYZ with bases ZY and WX, ZY = 4, YX = 10, and WX = 20. Y. D. Find height h…

A: Consider the given figure, First find value of EX. Lets assume EX=x As it is isosceles trapezoid, so…

Q: 3. Find the surface area of this cone. 5 m 12m B iU Font Family - AA A e=- E P Search

A:

Q: Find the volume of the sphere x? + y² + z² = a² (In Cartesian coordinate system).

A: To calculate the volume of the sphere, use the following formulae.…

Q: Use spherical coordinate to find the volume above the cone z² = x² + y and inside sphere x² + y? +…

A: The equation of cone is, z2=x2+y2 The equation of sphere is, x2+y2+z2=2az

Q: Given a lamina that occupies the region outside the circle r = 2 and inside the cardioid r = 2 +…

A: Given a lamina that occupies the region outside the circle r = 2 and inside the cardioid…

Q: The vertices of a triangle are at (0,0), (6,6), and (9,3) . What is the volume, in cubic units, of…

A: The figure by hand is show below of the given question:

Q: Refer to the figure and find the volume V generated by rotating the given region about the specified…

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Q: (a) Evaluate (x? + y?)" dA where R is the unit disk r2+ y? < 1.

A: The solution is given as

Q: The volume of the parallelepiped is Volume = |a x b||c|| sin o| = |(a x b)- c| %3D %3D True False

A: We have to check either the volume of parallelepiped is volume=a×bcsinϕ=a×b·c or not.

Q: 28 Describe the surface withe cylindrical equabion p?+z?=9. [ Oraw it and Solve it] .

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Q: Use polar coordinates to find the volume of the given solid. Inside the sphere x2 + y2 + z? = 25 and…

A: Solution =Volume of the given solid

Q: A grain silo has a cylindrical shape. Its radius is 7 ft, and its height is 33 ft.

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Q: Ged the volume and centroid generated by revolving the given plane area about the indicated axis. 1.…

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Q: 4. Use Maple to draw the torus whose equation in spherical coordinates is given by p= sin(ø), and…

A: Given Use Maple to draw the torus whose equation in spherical coordinates is given by ρ=sinϕ.

Q: 11- Find the volume of the solid that lies within both the cylinder x2 + y? = 1and the sphere x2 +…

A: In cylindrical coordinates the volume is bounded by cylinder r = 1 and sphere x2+y2+z2=4 We know…

Q: A. tor pedo has the Shape of a cutinder with area tshow the dimensions which aive manimam where…

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Q: Compute the volume of W using cylindrical coordinates.

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Q: The volume of the open cylindrical tank is

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Q: For a right circular cylinder, suppose that r= 6in and h= 7in Find the exact a) Lateral area L b)…

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Q: A storage bin has the shape of a cylinder with a conical top. What is the volume of the storage bin…

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Q: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of…

A: We know by the theorem of Pappu that the volume of a solid is obtained by area times the distance…

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: Let E be the solid enclosed by the sphere a? + y? + (z – 3)2 = 9 above the plane z = 2. The volume…

A: Given, Sphere : x2+y2+z-32=9Plane , z=2∫∫∫dV=∫02π∫0a∫bcρ2 sinϕ dρ dϕ dθ To find : Value of a,b,c