Answer:
case a) The approximate circumference of circle is
and the ratio of circumference to Diameter is 
case b) The approximate circumference of circle is
and the ratio of circumference to Diameter is 
case c) The approximate circumference of circle is
and the ratio of circumference to Diameter is 
Step-by-step explanation:
we know that
The approximate circumference of each circle, is equal to the perimeter of each inscribed polygon
case A) the figure is an inscribed pentagon
step 1
Find the approximate circumference of circle
The perimeter of the pentagon is equal to

where

substitute

therefore
The approximate circumference of circle is 
step 2
Find the ratio of circumference to Diameter
we know that
The radius is half the diameter so

The ratio is equal to

case B) the figure is an inscribed hexagon
step 1
Find the approximate circumference of circle
The perimeter of the hexagon is equal to

where

substitute

therefore
The approximate circumference of circle is 
step 2
Find the ratio of circumference to Diameter
we know that
The radius is half the diameter so

The ratio is equal to

case C) the figure is an inscribed dodecahedron
step 1
Find the approximate circumference of circle
The perimeter of the dodecahedron is equal to

where

substitute

therefore
The approximate circumference of circle is 
step 2
Find the ratio of circumference to Diameter
we know that
The radius is half the diameter so

The ratio is equal to

<em>Conclusion</em>
We know that
The exact value of the ratio
is equal to

The approximate value of the circumference will be closer to the real one when the number of sides of the inscribed polygon is greater