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

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