Find the volume of the solid that is enclosed by the cone z = and the sphere x² + y2 + z2 = 72.

Q: Calculate the volume of one of the wedge-like objects formed by cutting the cylinder x²+9y²=a² with…

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Q: Find the surface area of the part of the sphere x² + y² + z² = 81 that lies above the cone z =…

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Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

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: Describe in words the level curves of the top half of the sphere x2 + y2 + z2 = 1.

A: Top half of the sphere will be a hemisphere.

Q: 5. Identify and sketch the surfaces in space, 3-D. Must be in your handwriting. a) x² + y² =a² b)…

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Q: Evaluate ff. xyz ds, over that part of a sphere of two units radius and centre at the origin Which…

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Q: What is the area of the conic (x + 3) + y 25

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Q: Find the surface area of the part of the sphere x² + y² + z² = 16 that lies above the cone z = √√x²…

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Q: Find the volume of the tetrahedron formed by the intersection of the coordinate planes and the plane…

A: Given plane is

Q: Find the surface area of the part of the sphere x? + y² + z? = 4 that lies above the cone z = I² +…

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Q: 6) Find the area of the part of the sphere X² + y² + Z² = 4 that lies within the cylinder X² + y² =…

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Q: What is the definition of a parabolic cylinder?

A: The parabolic cylinder functions are the solutions to the differential equation d2ydx2 + ax2 + bx +…

Q: Find the surface area of the part of the sphere x² + y² + z² = 4 that lies above the cone z = x² +…

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Q: The sphere x² + 10x + y² +8y+z² − 2z = 34 is centered at the point (a, b, c). Find abc, the product…

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Q: Use spherical coordinates to find the volume of the top half of the sphere x2+y2+z2 = 4 that lies…

A: The required volume is given by triple integral is  ∫∫∫Rdv     …..(1) where E is the region on the…

Q: 2. a) Give a representation of the cylinder y2 + z² = 16,-2 ≤ x ≤ 3 as a parametric surface. b) Find…

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Q: The sphere x² + 10x + y² + 8y + z² - 2z = 34 is centered at the point (a, b, c). Find abc, the…

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Q: 2. Find the center and radius of the sphere *+y ++4x-2y+8-4 0

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