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).

Three graphs. Horizontal axis, diameter in meters, scale 0 to 10, by 2's. Vertical axis, scale 0 to 20, by 2's. 

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.

    Two squares and circle on a grid of 4 units by 4 units.

  2. Here is another picture of two squares and a circle. Use the picture to explain why the area of this circle is more than 18 square units and less than 36 square units.

    A square with a circle inside of it and a square inside of the circle. The shapes are drawn on a grid. 

Problem 6

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

A circle with center point A. Diameter CD, 15 cm. Points on the circle are C, E, G, B, D.
(From Unit 3, Lesson 3.)