Question

A. How long does the piece of wire need to be to make the shape? Explain.

B. Construct Arguments What information do you think is needed to find part of the circumference of a circle? Justify your answer

Answer 1

A. The wire needs to be 138.226 cm long but already 34.5565 cm of the circle has been covered.

B. To determine the length of the wire needed, we subtract a quarter of the circles circumference from its whole circumference.

Explanation:

Step 1:

The circumference of a circle is obtained by multiplying the radius with 2π.

The circumference of a circle
`= 2 \pi r.`

Here the radius of the circle is 22 cm but already a quarter of the circumference has been covered with wire.

Step 2:

So to determine the length of the wire needed, we subtract a quarter of the circles circumference from its whole circumference.

So the circumference of the circle
`= 2(3.1415)(22) = 138.226` cm.

`(3)/(4) (138.226) = 103.6695` cm and
`(1)/(4)(138.226) = 34.5565` cm.

So the wire needs to be 138.226 cm long but already 34.5565 cm of the circle has been covered. An additional 103.6695 cm of wire is needed to cover the remaining circle.