Find the volume of the solid bounded below by the plane z = 1 and above by the sphere x² + y² + z² = 3² Write your answer as a reduced fraction. Volume = π

Q: 1. Let S3 = {x² + y + 22 + w² = 1} be a 3-dimensional sphere. Write down the local coordinate and…

A: Sphere is given by  x2 + y2 + z2 + w2 = 1    =>  x2 + y2 + z2 = (1 - w2)    Comparing to standard…

Q: Could you find the area of the surface given the portion of the paraboloid in the first octant.

A: Determine the surface area of the surface bounded by the given paraboloid z in the first octant.

Q: Consider the parallelepiped with adjacent edges u = 8i + 4j + k v = i+j+9k w = i+ 9j + 4k Find the…

A:

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: Determine whether the set of vectors in P₂ is linearly independent or linearly dependent. S= (2-x,…

A:

Q: For any non negative integer n , prove that an − bn is divisible by a−b,where a and b are any…

A: answer

Q: the area of the surface. The part of the sphere x² + y² + z² = 81 that lies above the plane z = 6.

A: The solution is given by

Q: J (1,4) M(-1, 2) К(3,2) L (1, – 3)

A:

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 volume of the given solid. Enclosed by the paraboloid Z = 5x2 + 4y2 and the planes x = 0, y…

A: The region enclosed by planes

Q: Find the volume enclosed by the cy linder (x-1) ty²=1 and the sphere x² +y²7z²=L4.

A:

Q: find the volumes of the solids generated byrevolving the regions about the given axes. If you think…

A: Consider the following graph:

Q: Calculate the surface of cylinder x² + y² = 1 that lies between the Z=0 and == x1y+ 2 planes Fax is…

A: Given :Cylinder  x2+y2=1 that lies between the plane z=0 and z=x+y+2. To Find : Surface Area of the…

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

A:

Q: Part 2. Compute for the volume of the solid formed on the first quadrant of the cartesian plane…

A:

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 indicated region. the tetrahedron cut off from the first octant by the plane…

A: Let's find volume.

Q: the surface area E = 9(x1 4₁2)

A:

Q: 2√ab y y² = 4ax b X

A:

Q: 4. A sphere x² + y² + z² ≤ 4a² has a hole drilled through it in the shape x² + y² ≤ 2ax. How much of…

A:

Q: S is the lower portion of the sphere x2 + y2 + z2 = 25 cut by the cone z = √√√x² +

A: