# Lesson 7

Exploring the Area of a Circle

Let’s investigate the areas of circles.

### Problem 1

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:
radius (m), circumference (m), or area (m2).

### Problem 2

Circle A has area 500 in2. The diameter of circle B is three times the diameter of circle A. Estimate the area of circle B.

### Problem 3

Lin’s bike travels 100 meters when her wheels rotate 55 times. What is the circumference of her wheels?

(From Unit 3, Lesson 5.)

### Problem 4

Priya drew a circle whose circumference is 25 cm. Clare drew a circle whose diameter is 3 times the diameter of Priya’s circle. What is the circumference of Clare’s circle?

(From Unit 3, Lesson 3.)

### Problem 5

1. Here is a picture of two squares and a circle. Use the picture to explain why the area of this circle is more than 2 square units but less than 4 square units.

Point $$A$$ is the center of the circle, and the length of $$CD$$ is 15 centimeters. Find the circumference of this circle.