   Chapter 5.R, Problem 25E

Chapter
Section
Textbook Problem

# The height of a monument is 20 m. A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side 1 4 x meters. Find the volume of the monument.

To determine

To find:

The volume of a monument.

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=limni=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

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