Express the volume of the solid lying inside the sphere x? + y2 + z2 = 36 and outside the cylinder x2 + y² = 9 with triple integral in cartesian coordinates, cylindrical coordinates and spherical coordinates respectively.

Q: Describe the surfaces r = R in cylindrical coordinates and ρ = R in spherical coordinates.

A: Given cylindrical and spherical coordinates.

Q: Let S be the part of the sphere x^2 + y^2 + z^2 = 1 that lies above the conez = sqrt(x^2 + y^2).…

A: The objective of this question is to evaluate the surface integral of the function sqrt(x^2 + y^2)…

Q: what is the formula to find centroid of triangular prism

A: Centroid of triangular prism is determined as shown below.

Q: The four corners of a thin homogeneous and square plate with side 2a are folded up so that they…

A: It is given that the side length is 2a.Let the total mass of the system is M.

Q: Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone z = Vx² + y2…

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Q: Q8) Use cylindrical coordinates to find the volume of a curved wedge cut out from a cylinder (x -…

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Q: Evaluate ∫W z dV, where W is the first-octant portion of the solid sphere of radius 2 centered at…

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Q: Find the volume of the solid region which lies inside the sphere x² + y? + z² = 4z and outside of…

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Q: Use spherical coordinates to find the volume of a solid that lies above the xy- plane, outside the…

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Q: Express the volume of the solid lying inside the sphere r2 + y? + 22 8 and outside the cylinder ? +…

A: Given:  Solid lying in a sphere x2+y2+z2=16 and outside the cylinder  x2+y2=2

Q: Find the volume of the solid that lies within the sphere x² + y2 + z² = 25, above the xy-plane, and…

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Q: Use cylindrical coordinates to determine the volume of the solid that is enclosed by the cone z =…

A: Volume by cylindrical coordinates

Q: Calculate the volume of the sphere x^2 + y^2 + z^2 = a^2, using both spherical and cylindrical…

A: Given the equation of the sphere is       x2+y2+z2 = a2 ,where a is the radius of the sphere.

Q: Use spherical coordinates to find the volume of a solid that lies above the zy- plane, outside the…

A: The given 2 spheres are: x2+y2+z2=4…1x2+y2+z2=2z…2 The plane of intersection of the 2 spheres: To…

Q: Find the volume of rotated Gaussian about z-axis in cylindrical polar coordinates?

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Q: _(2²² + y² + z²)³/²dzdydx 1-z²-yª

A: Given ∫-11∫01-x2∫1-x2-y20(x2+y2+z2)32dzdydx Given instruction: To solve this integral convert…

Q: Find the surface area of that part of the plane 2x + 3y + z = 3 that lies inside the elliptic…

A: Given: The plane is: 2x+3y+z=3. The elliptic cylinder is: x225+y29=1. To Find: The surface area of…

Q: Use spherical coordinates to evaluate the triple integral ∫∫∫ √(x^2 + y^2 + z^2) dv where G is the…

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Q: Convert the integral from rectangular coordinates to both cylindrical and spherical coordinates |–x²…

A: Given triple integral, ∫01∫01-x2∫01-x2-y2zx2+y2dzdydx To convert this integral from rectangular…

Q: sphericity of cylindrical

A: Sphericity of the particle=φ=π136Vp23Ap Vp= volume of the particle Ap= surface area of the particle