Using the spherical coordinate evaluate a) , x? dv, where G is a solid region between the sphere x? + y? + z? = 4 andx? + y? + z? = 9

Q: b) M. dv, where G is the solid region that lies between the sphere x? + y? + r+y?+z? z2 = 36 and the…

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Q: Find the area of the surface. The part of the sphere x? + y2 + z? = 25 that lies above the plane z =…

A: We have given The part of the sphere x2 + y2 + z2 = 25 that lies above the plane z = 2.

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere- + y? +…

A: Solution :-

Q: Using spherical coordinates, the volume of the solid inside the sphere x+y+z -9 and above the plane…

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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: Evaluate [[ (x + y? +=?)2 dV, where 2 is the solid hemisphere (half of the sphere) enclosed by x +…

A: Change the given system to a spherical coordinate system and solve it.

Q: 9. Use spherical coordinates to find the volume of the part of the ballps 4 that lies between the…

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Q: Use polar coordinates to find the volume of the given solid. Inside the sphere x?+ y² + z² = 25 and…

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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: Let B be the sphere x2 + y? + z2 = 1. %3D The volume of the portion of B contained in the first…

A: x2+y2+z2=1

Q: FIs () Use spherical coordinates to evaluate 1- av where the solid E lies above the cone z=V+y*,…

A: We have to evaluate.I=∭Exzdv, using spherical coordinate  Consider, where the solid E lies above…

Q: Use spherical coordinates to find the volume of the solid that lies above the cone 0 = 7/3 and below…

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

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Q: Consider the parallelepiped with adjacent edges u = 3i + 2j + k v = i + j + 2k w = i + 3j + 3k (a)…

A: Let us consider the parallelepiped with adjacent edgesu = 3i + 2j + kv = i + j + 2kw = i + 3j + 3k…

Q: SSS, xz dV, where D is the solid region in the first octant bounded above by the sphere x + y? + z?…

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Q: Evaluate , x*+2y* D 2x++8y++2z+ dV, where D is the region enclosed by the spherical surface x2 + y?…

A: Given: To evaluate ∫∫∫D x4 + 2y42x4  + 8y4 + 2z4 dV  Where D is the region enclosed by the spherical…

Q: Use spherical coordinates to find the volume of the top half of the sphere x? + y? + z? = 4 that…

A: Given that a sphere x2+y2+z2=4 and a cone is z2=x2+y2 We have to find the volume of the top of the…

Q: Use spherical coordinates to find the volume of the solid enclosed by the sphere x2 + y² + z? = 4a?…

A: This question is about finding volume of solid enclosed by sphere. We can find it using triple…

Q: The volume in spherical coordinates for the solid that lies within the sphere p = 2 above the…

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Q: Use polar coordinates to find the volume of the given solid: i. Under the paraboloid ? = ?^2 + ?^2…

A: Given that       Under the paraboloid z = x2+y2 and above the disk x2+y2 ≤ 25. Here by using polar…

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

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Q: Using spherical coordinates, the volume of the solid inside the sphere x+y+z²=9 and above the plane…

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Q: The volume of the solid that lies above the cone z = V3/x2 + y? and below the sphere z = x? +y? + z2…

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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: If E is the region inside the sphere r2 + y? + z² = 4, below the cone z = /3x² + 3y², above z = gral…

A: Given If E is the region inside the sphere x² + y² + z² = 4, then the integral in spherical…

Q: Using spherical coordinates, the volume of the solid inside the sphere x²+y² +z² = 9 and above the…

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Q: 2. Find the volume of the solid formed by the region inside the sphere x? + y? + z? = 16 and outside…

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Q: b) Using Spherical Coordinates, find the volume of the solid G bounded above b x² + y? + z? = 25 and…

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Q: The volume in spherical coordinates for the solid that lies within the sphere p = 2 above the…

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Q: b) Write the equation of the sphere x² + y² + (z – 1)² = 1 in spherical coordinates then find the…

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Q: Let B be the sphere x? + y + z? = 4. The volume of the portion of B contained in the first octant is…

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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: Using spherical coordinates, the volume of the solid inside the sphere x + y +z? 9 and 3/3 is given…

A: and

Q: Using spherical coordinates, the volume of the solid inside the sphere x2+ y²+z2 =9 and above the…

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Q: Use polar coordinates to find the volume of the solid lying under the cone z = Vx2 • above the plane…

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Q: Evaluate [[[(x + y² +=?)? dV, where 2 is the solid hemisphere (half of the sphere) enclosed by x? +…

A: Solved below...

Q: Using the spherical coordinate evaluate a) ,x² dv, where G is a solid region between the sphere x² +…

A: The given integral is ∭Gx2 dV where G is a solid between the sphere x2+y2+z2=4  and x2+y2+z2=9.…

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

A: Sol

Q: Use spherical coordinates to find the volume of the region bounded by the sphere p= 20 cos q and the…

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Q: Use polar coordinates to find the volume of the given solid. Above the cone z = Vx2 + y2 and below…

A: The solid is bounded  above by   z=x2+y2 and below by the sphere x2+y2+z2=49. From z=x2+y2, z2=x2+y2…

Q: Consider the region D with y 20 and : 2 0 bounded by the cones 22 = ² + y? and the hemisphere z =…

A: Use the following formulae, to obtain the required result.…

Q: Find the surface area of the portion of the sphere x² + y? + z² = 8 that is cut out by the cone z =…

A: The objective is to find the surface area of the portion of the sphere x2+y2+z2=8 that is cut out by…

Q: Using spherical coordinates, the volume of the solid inside the sphere x+y? +z2 =9 and above the…

A: In spherical coordinates,  x=ρsinϕcosθ, y=ρsinϕsinθ, z=ρcosϕ, dxdydz=ρ2sinϕdρdϕdθ, x2+y2+z2=ρ2…

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X y² +…

A: We have to find the volume of the solid.

Q: Use a spherical coordinate integral to find the volume of the given solid. the solid between the…

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Q: Find the volume of the first-octant portion of the "wedge" of the sphere x? + y? + z? = 64 bounded…

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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