#### To determine

**To find:**

The volume of a monument.

#### Answer

12533m3

#### Explanation

**1) Concept:**

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

V=limn→∞∑i=1nAxi*∆x=∫abAxdx

**3) Given:**

Height of monument is 20m.

Side of equilateral triangle is x4m.

**4) Calculations:**

The equilateral triangles have angles of equal measure of 60°.

The height of equilateral triangle =32·side of triangle

=32·x4

=3x8m.

Therefore, the area of the equilateral triangle is

=12x43x8=3 x264.

Since the height of the monument is 20m, to find volume, integrate area from 0 to 20.

V= ∫020Axdx

That is,

V=∫0203x2 64 dx

After integrating,

V=364x3320 0

Applying the Fundamental Theorem of Calculus,

V=3642033-0=12533

**Conclusion:**

Volume of monument =12533m3