Lesson 15

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

A circle’s circumference is approximately 76 cm. Estimate the radius, diameter, and area of the circle.

Problem 3

Jada paints a circular table that has a diameter of 37 inches. What is the area of the table?

Problem 4

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 5, Lesson 12.)

Problem 5

The Carousel on the National Mall has 4 rings of horses. Kiran is riding on the inner ring, which has a radius of 9 feet. Mai is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is.

  1. In one rotation of the carousel, how much farther does Mai travel than Kiran?

  2. One rotation of the carousel takes 12 seconds. How much faster does Mai travel than Kiran?

(From Unit 5, Lesson 13.)