Question

circle parts and circumference

• indicates required question

1. explain the difference between radius and diameter in your own words. *
2. if a circle has a radius of 8 cm, what is its diameter? show your thinking. *
3. a bicycle wheel has a diameter of 24 cm. calculate its circumference using π ≈ 3.14. explain each step.
4. compare and contrast a chord and a diameter. how are they similar and different? * you will have to look up what a chord is in relation to a circle.
5. a pizza has a radius of 16 cm. if you want to put a decorative border around the edge, how much border material do you need? show your calculation.
6. explain why the circumference formula c = πd works. what does each part represent?

Explanation:

Question 2

Step1: Recall the relationship between radius and diameter.

The diameter \( d \) of a circle is twice the radius \( r \), so the formula is \( d = 2r \).

Step2: Substitute the given radius into the formula.

Given \( r = 8 \) cm, then \( d = 2\times8 = 16 \) cm.

Step1: Recall the formula for the circumference of a circle.

The formula for the circumference \( C \) of a circle is \( C=\pi d \), where \( d \) is the diameter and \( \pi\approx3.14 \).

Step2: Substitute the given diameter into the formula.

Given \( d = 24 \) cm and \( \pi\approx3.14 \), then \( C = 3.14\times24 \).

Step3: Calculate the product.

\( 3.14\times24 = 75.36 \) cm.

Step1: Find the diameter from the radius.

The radius \( r = 16 \) cm, so the diameter \( d = 2r=2\times16 = 32 \) cm.

Step2: Recall the circumference formula.

The formula for the circumference \( C \) of a circle is \( C = \pi d \) (or \( C = 2\pi r \)). Using \( C=\pi d \) with \( d = 32 \) cm and \( \pi\approx3.14 \).

Step3: Substitute and calculate.

\( C=3.14\times32 = 100.48 \) cm.

Answer:

The diameter of the circle is 16 cm.

Question 3