Set up the triple integral needed to compute the volume of the tetrahedron bounded by the plane 24x + 32y + 12z - 96 = 0 and the coordinate planes.

Q: Find the volume of the largest box of the type shown in the figure, with one corner at the origin…

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

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Q: The points O, A, B, C have coordinates (0,0,0), (a, 0,0), (0, b, 0) and (0,0, c) respectively, where…

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Q: Find the volume of the tetrahedron bounded by coordinate planes (x>=0, y>=0,z>=0) and the plane…

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Q: A tetrahedron is built and is bounded by the coordinate planes and the plane 3x+2y+6z=18. How would…

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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: The base of a solid is a square with vertices located at (1, 0),(0, 1),(−1, 0), and (0, −1). Each…

A: Given,

Q: How to calculate the volume of a complex 3D figure that has both spherical and flat parts?

A: Given: A complex 3D shape has both spherical and flat part. To determine: Method for finding volume…

Q: Find the centroid of the region cut from the first quadrant by the circle x² + y² = 81. The…

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Q: Determine the volume of a triangular prism with vertices at A(-1,1,3), B(-1,0,0), C(2,0,0) and D…

A: 1:  2:

Q: Use Pappus's theorem for surface area and the fact that the surface area of a sphere of radius d is…

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