Developments and Envelopments (Leaving Cert DCG): Flashcards

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Envelopments
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Envelopments definition

Wrapping a flat pattern around an object to create a 3D shape

Relationship between envelopment and development

Envelopment is opposite of development

Complete envelopments

Wrapping entire development around 3D object

Partial envelopments

Only part of object's surface is covered

Circumference formula for cylinder (radius RR)

2πR2\pi R

Cylinder development length requirement

Must equal circumference: 2πR2\pi R

Flat development pattern requirement

Must contain all surfaces to cover object

Purpose of fold lines in envelopment

Indicate where pattern bends to form 3D shape

Example of partial envelopment application

Labels on bottles and jars

Partial envelopments when laid flat

Look more complex when flattened than when wrapped on object

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