Mass from density data The following table gives the density (in units of g/cm2) at selected points (in polar coordinates) of a thin semicircular plate of radius 3. Estimate the mass of the plate and explain your method.
Given:
The density of the points is given for selected points of thin semi-circular plate is shown below,
The semi-circular plates are drawn for different radii’s is shown below,
From the above diagram, it is observed that the plate is divided into 12 parts. Consider the 4 parts divided by r = 1 and the lines are given as follows,
These four parts are sectors of the circle of radius r = 1. Therefore, denote the mass of these four parts as m1
The area of the sector is expressed as,
Thus, the mass of the region is expressed as,
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