Use cylindrical coordinates to find the volume of a solid bounded below by the cylinder æ +y <. and xy-plane and above by the paraboloid z = 9 – x² – y?.

Q: The volume of the solid generated by revolving the region bounded by x+ 2y =2, y=0, and x=0, about…

A: I use shell method to find volume about x axis

Q: Find the volume of the region bounded below by the cone ( =V(x² + y²) ‚and above the plane ( z=1),…

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Q: Find the volume of the solid generated bounded byx = Jy – 2, x = y2 – 4y + 4, rotated about the x-…

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Q: Use cylindrical coordinates to find the volume of the solid bounded by the paraboloid of revolution…

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Q: Q:1) Find the volume bounded below Z1=x2+y? and above by Paraboloid Z3= 8-x²-y² by using cylindrical…

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Q: Use the shell method to find the volume of the solid generated by revolving the plane region about…

A: Find the volume of the solid by using shell in method  Given line x=6 y=x,y=0 ,x=4

Q: Consider the solid generated by the surfaces in the 1st octant ?+y?+zZ =4 y?+2 = 2 Find the triple…

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Q: The volume of the solid bounded above by the paraboloid z = 4 – x? – y? and bounded below by the…

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Q: Using eylindrical coordinates, the volume of the solid bounded above by : =1 and below by zx + y 18:…

A: To find the volume of the solid bounded above by z=1 and below by z=x2+y2, using cylindrical…

Q: Find the volume of the solid obtained by rotating the region bounded by * = 6y', y = 1, r = 0, about…

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Q: Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2 + y?, below…

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Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A: Given that the region bounded by the given curves about the x axis is       x = -3y2 + 12y - 9 ,…

Q: Find the volume of the region enclosed by the cylinder x2 + y? = 2, the plane z – x+ y= 0 and the…

A: We have,

Q: Find the volume of the solid generated bounded by x = /y - 2, x y? – 4y + 4, rotated about the x-…

A: Washer Method : If f(x) and g(x) are two continuous non-negative function on a,b and f(x)≥g(x) on…

Q: Find the volume of the solid bounded below by the circular paraboloid z = x? + y? and abov the…

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Q: Find the volume of the solid that is bounded above by the cone x² + y² and below by the ry-plane and…

A: The given equation of cone is, z=x2+y2Apply the squaring both side into the given…

Q: Use the shell method to find the volume of the solid generated by revolving the plane region about…

A: Given: y=xy=0x=1

Q: Find the volume of the solid bounded by the paraboloids z = - 4+ a2 + y? and z = 3 - 2a2-2y? . Round…

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

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Q: Use a triple integral in cylindrical coordinates to find the = z and below by the volume of the…

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Q: Find the volume of the solid bounded by the paraboloid z= 23 -x -y and the plane z= 22 V = (Type an…

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Q: A solid is in the first octant lies inside the hemisphere z = V4 – x2 – y?, outside the cone z = Vx2…

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Q: Find the volume of the solid generated bounded by x = Jy – 4, x = y? – 8y+ 16, rotated about the Y -…

A: Washer Method :  If the function f(x) and g(x) be two continuous function and non-negative a,b and…

Q: 27T 5. = y² and x + y = 2 is revolved about y = 1. (Answer: c. u.)

A: Solution is given below:

Q: Use cylindrical coordinates to find the volume of the solid that is bounded above by the sphere x2…

A: sphere⇒x2+y2+z2cone⇒z=x2+y2   let x=ρ sinϕ sinθy=ρ sinϕ sinθz=ρ cosϕ sphere⇒ρ=1cone⇒ρ cosϕ=ρ…

Q: Use cylindrical coordinates to find the volume of the solid bounded by the paraboloid of revolution…

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Q: Use cylindrical coordinates to find the volume of the solid that is bounded above by z = 6 and below…

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Q: Use the washer method to find the volume of the solid of revolution for the region bounded by…

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Q: Find the volume of the solid which is under the surface z = 16 – x² – y and above the plane z = 8.

A: Given

Q: Use cylindrical coordinates to find the volume of the solid. Solid bounded above by z = 18 - x² – y?…

A: The objective is to find the volume of the solid bounded above by z=18-x2-y2 and below by z=x2+y2…

Q: Find the volume of the solid generated bounded by x = Vy – 2, x = y2 – 4y + 4, rotated about the %3D…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: Find the volume of the solid under the cone z = Va2 + y? and above the disk r² + y² < 4.

A: Volume, by using double integral

Q: Find the volume of the solid that lies within the sphere x2 + y2 + z² = 36, above the xy-plane, and…

A: The sphere is x2+y2+z2=36 and cone is z=x23+y23. Substitute x=ρsinϕcosθ,y=ρsinϕsinθ,z=ρcosϕ in…

Q: Use cylindrical coordinates to find the volume of the solid. Solid bounded by the graphs of the…

A: We need to find volume of solid.

Q: Find the volume of the solid formed by revolving the region bounded by the curves x = 0 and -3y +…

A: We will find out the required volume of solid of the revolution.

Q: B) Find the volume of the solid bounded by the cylinders r = y, z = y² and the planes, x = 0 and z =…

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Q: Find the volume bounded below by the paraboloid z= x? + y & above by the plane z=2y ?

A: The volume for the given question has been obtained in step 2.

Q: Find the volume of the solid bounded from above by the paraboloid z = 6 – a2 – y?, inside the…

A: In general volume, integrals are triple integral, which involves the integral with respect to x,y,…

Q: Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 9, above the xy-plane, and…

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Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: 2. Use cylindrical coordinates to find the volume of the solid that is below the paraboloid z = 2-x²…

A: Cylindrical coordinate system x=rcosθ, y=rsinθ , z=zdV=r dz dr dθ        (dV = dx dy dz) first we…

Q: Use the shell method to find the volume of the solid generated by revolving the plane region about…

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Q: Find the volume of the solid generated bounded by x = Jy – 1, x = y? – 2y + 1, rotated about the x-…

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Q: Use spherical coordinates to find the volume of the solid. Solid bounded above by x + y + z? = 36…

A: From spherical coordinates to rectangular coordinates:x=ρ sin ϕ cos θy=ρ sin ϕ sin θz=ρ cos ϕ From…

Q: Find the volume of the solid that lies within the sphere x2 + y² + z² = 64, above the xy-plane, and…

A: To find the volume if the solid within the given sphere above xy-plane and below the cone:…

Q: Find the volume of the portion of the solid cylinder x2 + y2&lt;= 1 that lies between the planes z =…

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Q: Use the method of cylindrical shells to find the volume of the solid generated by rotating the regi…

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Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

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