How to Calculate Cross Section Area

Written by pearl lewis
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How to Calculate Cross Section Area
Cross-sectioning a sphere produces a circle. (Jupiterimages/Photos.com/Getty Images)

Slice through any three-dimensional object and you produce a two-dimensional, internal view of the object. When slicing or sectioning at exactly 90 degrees to the primary axis of the object, a cross section is created. Cross sections of symmetrical objects are typically simple geometric shapes like circles and rectangles. The area of the cross section is a function of the dimensions of the two-dimensional view. Measurement of these dimensions provides the data required to calculate the object's cross-sectional area.

Skill level:
Moderate

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Things you need

  • Ruler
  • Calculator

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Instructions

  1. 1

    Identify the axis of symmetry for the object. For example, the axis of symmetry for a cylinder is the imaginary line directed down the middle and extending the length of the cylinder.

  2. 2

    Imagine a plane oriented perpendicular to the symmetry axis slicing through the object. The intersection of the plane with the object forms a two-dimensional projection on the plane.

  3. 3

    Identify the geometric shape formed by the projection of the object on the cross-sectional plane. For example, the cross section of a sphere or a cylinder is a circle, while the cross section of a cube will be a square.

  4. 4

    Measure the dimensions of the geometric shape using the ruler. For example, for a circular shape, measure the radius. If the shape is rectangular, measure the width and length of the rectangle.

  5. 5

    Calculate the cross-sectional area by determining the area of the geometric shape. For a rectangle, multiply adjacent side lengths using this formula: area = length x width. For a circle, the area = (3.14) x radius x radius. For example, the cross-sectional area of a wire with a radius of 0.1 inch is: area = (3.14) x (0.1) x (0.1) = 0.0314 inches squared.

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