Estimate the Area of a Circle.
In a previous lesson, you established the relationship between the diameter and circumference of a circle.
(1.) How is this graph the same?
(2.) How is it different?
Explore the Area of a Circle.
(1.) What shape does the figure look like when you rearrange the bisected parts?
(2.) What does the figure begin to look like?
(3.) What are the dimensions of the new shape?
(4.) What is the formula for the area of that shape?
Explore the Area of a Circle in Relation to the Diameter.
Here is a picture of two squares and a circle.
(1.) Use any tools in the applet above that can help you to explain why the area of the circle is more than 2 square units but less than 4 square units.
Here is another picture of two squares and a circle.
(2.) Use any tools in the applet above that can help you to explain why the area of this circle is more than 18 square units and less than 36 square units.
Here is a square whose side length is the same as the radius of the circle.
How many of these squares do you think it would take to cover the circle exactly?
Point A is the center of the circle, and the length of C D is 15 centimeters. Find the circumference of this circle.
The x-axis of each graph has the diameter of a circle in meters. Label the y-axis on each graph with the appropriate measurement of a circle by dragging the labels.