Geometry: Parallel Line and Radial Line Development

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Questions and Answers

What is the primary purpose of dividing the surface into a series of parallel lines in parallel line development?

  • To find the surface area of the shape
  • To create a two-dimensional representation
  • To determine the shape of a pattern (correct)
  • To calculate the volume of the shape

What type of shapes are suitable for radial line development?

  • Cube and rectangular prism
  • Sphere and hemisphere
  • Prism and cylinder
  • Cone and pyramid (correct)

What is the characteristic of elements in a developed cylinder?

  • They are parallel and perpendicular to the base (correct)
  • They are diagonal and parallel to the top
  • They are curved and parallel to the development plane
  • They are radial and perpendicular to the base

What is the condition for a shape to be suitable for parallel-line development?

<p>It must have parallel lateral edges or elements (A)</p>
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What is the shape of the base and top of a developed cylinder?

<p>Circle (A)</p>
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What is the orientation of the cylinder during development?

<p>One element lies on the development plane (B)</p>
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Flashcards

Purpose of parallel lines in pattern development?

Determines the shape and size needed for a flat pattern that can be formed into the desired 3D object.

Shapes for Radial Line Development?

Shapes that converge at a single point, like cones or pyramids, are suitable for radial line development.

Developed Cylinder Element Characteristics?

Elements are parallel to each other and perpendicular to the circular bases.

Parallel-Line Development Condition

The shape must be of a form where the sides are parallel to each other.

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Developed Cylinder Base and Top Shape?

The base and top of a developed cylinder are circles.

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Cylinder Orientation During Development?

One element of the cylinder must be in direct contact (lies on) the flat plane that it is being drawn/developed on.

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Study Notes

Parallel Line Development

  • Uses parallel lines to construct the expanded pattern of 3D shapes.
  • Divides the surface into a series of parallel lines to determine the shape of a pattern.
  • Examples: Prism, Cylinder.

Radial Line Development

  • Uses lines radiating from a central point to construct the expanded pattern of 3D shapes.
  • Examples: Cone, Pyramid.

Characteristics of Parallel-Line Developments

  • Made from common solids composed of parallel lateral edges or elements.
  • Examples: Prisms and cylinders.
  • The cylinder is positioned with one element lying on the development plane.
  • The cylinder is unrolled until it is flat on the development plane.
  • The base and top of the cylinder are circles, with a circumference equal to the length of the development.
  • All elements of the cylinder are parallel and perpendicular to the base and the top.
  • When cylinders are developed, all elements are parallel and any perpendicular section appears as a stretch-out line perpendicular to the elements.

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