Se polar coordinates to find the volume of the given solid. the solid above the xy-plane that lies below the ellipsoid 4x2 + 4y2 + z2 = 64 but inside the cylinder x2 + y2 = 4

The volume of the solid inside the cylinder and the ellipsoid and above the xy-plane is cubic units.

The volume of a solid in cylindrical coordinates () can be determined by the following triple integral:

(1)

The solid is constrained by the following equations in cylindrical coordinates:

Cylinder

(2)

Ellipsoid

(3)

The integration limits can be identified by using the following intervals:

, ,

And the triple integral is the following form:

Now we proceed to integrate the expression thrice:

The volume of the solid inside the cylinder and the ellipsoid and above the xy-plane is cubic units.

We kindly invite to check this question on triple integrals: link

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.