The formula to calculate the perimeter of a rectangle given its length and the diameter of its circumcircle is:
\[ P = 2 \left( l + \sqrt{D_c^2 - l^2} \right) \]
Where:
The perimeter of a rectangle is the total length of all the boundary lines of the rectangle.
The length of the rectangle is any one of the pair of parallel sides which are longer than the remaining pair of parallel sides.
The diameter of the circumcircle of the rectangle is the diameter of the circle which contains the rectangle with all its vertices lying on the circle.
Let's assume the following values:
Using the formula:
\[ P = 2 \left( 8 + \sqrt{10^2 - 8^2} \right) \approx 28 \, \text{meters} \]
The perimeter is approximately 28 meters.
| Midsphere Radius (meters) | Surface to Volume Ratio (1/meter) |
|---|---|
| 1 | 3.674234614174767 |
| 1.5 | 2.449489742783178 |
| 2 | 1.837117307087383 |
| 2.5 | 1.469693845669907 |
| 3 | 1.224744871391589 |
| 3.5 | 1.049781318335648 |
| 4 | 0.918558653543692 |
| 4.5 | 0.816496580927726 |
| 5 | 0.734846922834953 |
| 5.5 | 0.668042657122685 |
| 6 | 0.612372435695795 |