What is the volume of the solid given the base of a solid is the region in the first quadrant bounded by the graph of #y=-x^2+5x-4^ and the x-axis and the cross-sections of the solid perpendicular to the x-axis are equilateral triangles?
1 Answer
The volume is
The curve
For
The solid itself looks something like this:
Now draw the cross-section equilateral triangle, label the sides
By the Pythagorean Theorem,
so that
The cross-sectional area is
Continuing to simplify gives