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lozanna [386]
3 years ago
6

Part I: Measuring Parts of a Circle

Mathematics
1 answer:
cluponka [151]3 years ago
4 0

Answer:

case a) The approximate circumference of circle is 5.9\ units and the ratio of circumference to Diameter is \frac{C}{D}=2.95

case b) The approximate circumference of circle is 6\ units and the ratio of circumference to Diameter is \frac{C}{D}=3

case c) The approximate circumference of circle is 6.24\ units and the ratio of circumference to Diameter is \frac{C}{D}=3.12

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

P=5s

where

s=1.18\ units

substitute

P=5(1.18)=5.9\ units

therefore

The approximate circumference of circle is 5.9\ units

step 2

Find the ratio of circumference to Diameter

we know that

The radius is half the diameter so

D=2r=2(1)=2\ units

The ratio is equal to

\frac{C}{D}=5.9/2=2.95

case B) the figure is an inscribed hexagon

step 1

Find the approximate circumference of circle

The perimeter of the hexagon is equal to

P=6s

where

s=1\ units

substitute

P=6(1)=6\ units

therefore

The approximate circumference of circle is 6\ units

step 2

Find the ratio of circumference to Diameter

we know that

The radius is half the diameter so

D=2r=2(1)=2\ units

The ratio is equal to

\frac{C}{D}=6/2=3

case C) the figure is an inscribed dodecahedron

step 1

Find the approximate circumference of circle

The perimeter of the dodecahedron is equal to

P=12s

where

s=0.52\ units

substitute

P=12(0.52)=6.24\ units

therefore

The approximate circumference of circle is 6.24\ units

step 2

Find the ratio of circumference to Diameter

we know that

The radius is half the diameter so

D=2r=2(1)=2\ units

The ratio is equal to

\frac{C}{D}=6.24/2=3.12

<em>Conclusion</em>

We  know that

The exact value of the ratio \frac{C}{D} is equal to

\frac{\pi D}{D}=\pi

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

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