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The Volume of the given solid using polar coordinate is:
V=
<h3>What is Volume of Solid in polar coordinates?</h3>
To find the volume in polar coordinates bounded above by a surface z=f(r,θ) over a region on the xy-plane, use a double integral in polar coordinates.
Consider the cylinder, and the ellipsoid,
In polar coordinates, we know that
So, the ellipsoid gives
4() +
= 64
= 64- 4(
)
z=±
So, the volume of the solid is given by:
V=
=
To solve the integral take, = t
dt= -8rdr
rdr =
So, the integral become
=
=
=
so on applying the limit, the volume becomes
V=
=
V =
Since, further the integral isn't having any term of .
we will end here.
The Volume of the given solid using polar coordinate is:
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