In cylindrical coordinates, find the volume of the solid S enclosed by the cone and the sphere as shown, where z = r, and the upper hemisphere is the sqrt(2-r²): (0,0,√2) X x² + +y²+z² = 2 2 Z=√x + y

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 that lies under the sphere: x2 +y? +z? -2z=0 and above the cone: z=3(x²…

A: Solid lies under the sphere x2+y2+z2-2z=0⇒x2+y2+z-12=1 and above the cone z=3x2+y2 Now z=3x2+y2 and…

Q: Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone z = x² + y2…

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Q: Use cylindrical coordinates. Find the volume of the solid that lies between the paraboloid z = x2 +…

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Q: The volume of the solid given by the two surfaces is she = 8-3(x? + y*), z = (x² +y?)2 2

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Q: (c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3,2, 4), and w=(-6,1,1). V (i) Find the…

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Q: Use spherical coordinates to find the volumes of the two solids obtained when the hemisphere z =…

A: Let  x=rsinθcosφy=rsinθsinφz=rcosθJ=∂x,y,z∂r,θ,ϕ=r2sinθdrdθdϕ The plane x=3 divide the hemisphere…

Q: A section of a sphere is described by 0 <R< 3, 0 < 0 <™/2, and "/4 < Ø<™/2: Find: i. the surface…

A: Use the following formulae, to calculate the surface area and the volume of the sphere.

Q: Find the surface area of the part of the sphere x2+y2+z2=49 that lies above the cone z=(x2+y2)1/2

A: Consider the provided question,

Q: Determine the coordinates of the centroid of the trapezoidal area shown. Assume a = 290 mm, b = 405…

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Q: A wedge is cut out of a circular cylinder of radius 14 by two planes. One plane is perpendicular to…

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Q: Find the volume of the solid enclosed by the parabolics Z= 4CX²+y²² Jand 2 = 32- 4(x² + y²)

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Q: Find the volume of the solid that lies within the sphere x² + y² + z² = 4, above the xy plane, and…

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Q: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant

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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 coordinates. Find the volume of the solid that lies within both the cylinder  x2 +…

A: To find the volume of the solid that lies within both the cylinder and the sphere.…

Q: Find the volume of the solid that lies within both the cylinder x² + y² = 4 and the sphere x² + y² +…

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Q: Find the volume of the prism whase base is the triangle in te Xy-plane bonnded by the X-axis and the…

A: To find- Find the volume of the prism whose base is the triangle in the xy-plane bounded by the…

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

A: Volume by cylindrical coordinates

Q: Find the volume of the solid enclosed between the cone z = hr? and the plane z = 2h.

A: The variables in cylindrical coordinate systems are r, z and θ. In this problem, we have to find the…