Question

How would you use a model to determine the approximate formula for the circumference of a circle with a diameter of 8 cm, and connect the model to the actual formula?

Answer 1

Sorry for the late response, but the formula would be:

Circumference = pi x diameter
Circumference = 3.14 x 8
Circumference = 25.12

Hope this helps!!

Answer 2

Answer with explanation:

Take a thread of length x cm.Convert it into circle of radius r cm.

If you divide the Length of circle by value equal to 2 π, you will obtain radius of the circle.The value 2π is a constant Quantity is an Irrational number.

$\rightarrow \frac{\text{Length of thread}}{2 \pi}=r\\\\ \rightarrow \frac{x}{2 \pi}=r\\\\ \rightarrow x=2 \pi r$

Diameter of Circle =8 cm

Circumference of a circle with a diameter of 8 cm has radius equal to 4 cm because radius is half of diameter

           =2 × 3.14 × 4 cm

          = 25.12 cm

⇒So, Actual Length of thread =25.12 cm

Irrational Quantity=2 π=2×3.14=6.28 cm

So Radius

       $=\frac{25.12}{6.28}\\\\=4 cm$

Diameter =Radius × 2

            =4 cm × 2

          = 8 cm