Respuesta :
In the spherical coordinate system, the volume of a sphere can be calculated mathematically as the integral of an infinitely small volume element.
This feature is: d V is equal to r 2 sin d d r. Joining concerningϕgives2π, joining concerningθ gives 2 and joining concern in grgivesr 33.
Therefore, the sphere's volume is: V=4r3π3.
The same method is used to determine the cylinder's volume; however, we integrate the volume element in cylinder coordinates. This component is:
d V = d, d, and z.
In the x, y plane, is the radial coordinate. The cylinder's volume is determined by integrating it:
V is equal to r 2 h, where h is the height of the cylinder and r is the radius of the cylinder's base.
To learn more about cylinder coordinates here
https://brainly.com/question/14867188
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Full Question = Kepler's Wine Barrel Problem: What are the radius and height of the cylinder of largest volume that can be inscribed in a sphere of radius 6 as shown in the figure to the right?
radius = ? (ft)
height = ? (ft)
