Part i: measuring parts of a circle a. dakota with her homework. use diagrams of inscribed polygons to approximate the circumference of each circle. assume that all of the circles have a radius of 1. then, calculate the ratio of the approximate circumference to the diameter.

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

Conclusion

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

step-by-step explanation:

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