What is the effect of increasing the diameter of an implant by 25% on the surface area?

Prepare for the Oral and Maxillofacial Surgery (OMFS) Board Exam with flashcards and multiple choice questions. Each question offers hints and explanations. Ace your board exam!

When considering the effect of increasing the diameter of an implant, it's important to recognize that the surface area of a cylindrical object, such as a dental implant, is calculated using specific geometric principles.

The surface area of a cylinder is given by the formula:

[ \text{Surface Area} = \pi \times d \times h + 2 \times (\pi \times (d/2)^2) ]

Where ( d ) is the diameter and ( h ) is the height of the implant.

When the diameter increases by 25%, the new diameter can be expressed as ( 1.25d ). The surface area is thus dependent on the square of the diameter because the surface area involves terms that include ( d^2 ).

If we look at the surface area in relation to the diameter, the increase in the surface area can be calculated as:

  1. The original surface area is proportional to ( d^2 ).
  2. The new diameter leads to a new surface area proportional to ( (1.25d)^2 ), which simplifies to ( 1.5625d^2 ).
  3. This indicates that the new surface area is 1.5625 times the
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