Here we can see that the blue line cuts exactly half way through the angle that the black line makes with x axis
That is all the x values are halved
Which implies all the x value of the black line are divided by 2 to form the points on the blue line
so that give us the function
The volume of the region R bounded by the x-axis is:
If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.
From the given graph:
The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:
here:
Suppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8) from the graph, we have:
y = 4x
Now, our region bounded by the three lines are:
Similarly, the change in polar coordinates is:
where;
Therefore;
Then:
Learn more about the determining the volume of solids bounded by region R here:
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