The following diagram shows the graph of the function defined by as well as the graph of for a function , with both functions defined for all
Points and are the non-negative -axis intercepts of f, while is the local maximum on the graph of . Point is the point of intersection between the graphs of and . The shaded region R represents the area between the graph of and the -axis. The shaded region represents the area above the positive -axis between the graphs of and .
Find the coordinates of , and , giving your answers correct to three significant figures.
The graph of is a parabola with -intercepts and , and vertex
Find an expression for .
Hence find the area of region R.
The following diagram shows a cylindrical log with a wedge cut from it. The area of the major sector is equal to the area of the shaded region S. The length is equal to the distance between points E and F on the diagram above
Find the volume of the log.
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