Question

find the mass of the region bounded by ellipsoid x2/a^2 + y^2/b^2 + z^2/c^2 =1 if the density varies of the square of the distance from the centre.

Answer 1

Answer:

Step-by-step explanation:

In the same way that a circle turns into a solid sphere, an ellipse can become a solid "ellipsoid".

equation of ellipsoid

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}$

where

a,b and c is in real number, It is the distance of the axis in x, y and z direction

so,

volume of the ellipsoid = $\dfrac{4}{3}\pi$

Answer 2

Answer:

The volume of the ellipsoid =$\frac{4}{3} \pi$

Explanation:

An ellipse may transform into a solid "ellipsoid," similar to how a circle transforms into a solid sphere.

Equation of ellipsoid $=\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} }$

Here,

A,b,c are real numbers

x,u,z are directions,

Which in turn makes,

The equation of ellipsoid as $\frac{4}{3} \pi$

Ellipsoid:

• A sphere may be deformed into an ellipsoid by applying directed scalings, or more broadly, an affine transformation, to it.
• A quadric surface, or surface that can be described as the zero sets of a polynomial of degree two in three variables, is an ellipsoid.
• An ellipsoid among quadric surfaces has one of the two characteristics listed below.
• Every cross-section of a flat surface is either an ellipse, empty or reduced to a single point (this explains the name, meaning "ellipse-like").
• It can be contained in a sphere that is big enough since it is bounded.

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