Question

Find the volume of the solid bounded
by z=x²+y²=2, z=10-x²-y² and x²+y² = 1. Leave your answer correct to two decimal places. ​

Answer 1

Answer:

Volumes of Solids Using Double Integrals:

The volume of the solid bounded by two surfaces can be found by using double integration. If a solid is bounded above by one surface f(x,y,z)f(x,y,z) and below by another surface g(x,y,z)g(x,y,z), then the volume of this solid is given by

V=∬D(f(x,y)−g(x,y))dAV=∬D(f(x,y)−g(x,y))dA,

where DD is the region in the xyxy-plane defined by the intersection of the surfaces,

dA=dx dy or dA=dy dxdA=dx dy or dA=dy dx in rectangular coordinates, and dA=r dr dθ or dA=r dθ drdA=r dr dθ or dA=r dθ dr in polar coordinates.

Answer and Explanation: 1

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Given data

The solid is bounded by the paraboloid z=x2+y2z=x2+y2 and the plane z=9z=9.

The volume of the region bounded by...

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