The volume of a monument.
Use the definition of volume.
2) Definition of volume:
Let S be a solid that lies between x=a and x=b. If the cross sectional area of S in the plane Px, through x and perpendicular to the x-axis, is A(x), where A is continuous function, then the volume of S is
Height of monument is 20m.
Side of equilateral triangle is x4m.
The equilateral triangles have angles of equal measure of 60°.
The height of equilateral triangle =32·side of triangle
Therefore, the area of the equilateral triangle is
Since the height of the monument is 20m, to find volume, integrate area from 0 to 20.
V=∫0203x2 64 dx
Applying the Fundamental Theorem of Calculus,
Volume of monument =12533m3