Discovering the Area of a Circle with a Hula Hoop Activity

Hula hoop (or any large circular object)
Tape measure
String (optional for circumference measurement)
Scissors (if using string)
Calculator
Large sheet of paper or sidewalk chalk (optional, for visualizing area)
Introduction:

Discuss the goal of the activity: to understand the relationship between the circumference and area of a circle by measuring a hula hoop.
Briefly review the formulas for circumference (
�
=
2
�
�
C=2πr) and area (
�
=
�
�
2
A=πr
2
) of a circle.
Measuring the Circumference:

Allow students to use a tape measure to find the circumference of the hula hoop.
Alternatively, students can use a piece of string: wrap the string around the hula hoop, mark the length, then measure the string with a tape measure.
Finding the Radius:

Once the circumference is measured, guide students to use the circumference formula to find the radius.
�
=
�
2
�
r=
2π
C
​

Provide a calculator to help students with the division and multiplication involved.
Calculating the Area:

With the radius determined, guide students to use the area formula to find the area of the hula hoop.
�
=
�
�
2
A=πr
2

Allow students to perform the calculation using a calculator.
Visualizing the Area (Optional):

If possible, use a large sheet of paper or sidewalk chalk to draw the hula hoop.
Have students shade in the area to visualize the concept of the area of a circle.
Discuss how the area inside the circle represents all the space within the circumference.
Discussion and Reflection:

Discuss the process and what students discovered about the relationship between the circumference and the area.
Reinforce the importance of the radius in calculating both circumference and area.
Highlight how understanding these relationships is important in various real-world applications, such as engineering and design.
What Happened?

Students measured the circumference of a large circular object and used it to find the radius.
Using the radius, they calculated the area of the circle, reinforcing the geometric concepts and relationships between circumference, radius, and area.
Explore More:

Encourage students to try measuring and calculating the area of different circular objects.
Discuss how these measurements and calculations can be useful in practical scenarios, such as determining the amount of material needed to cover a circular area.