Video solutions to help Grade 7 students learn how to how to develop the definition of circle using diameter and radius.

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Common Core For Grade 7

Lesson 16 Student Outcomes

• Students learn how to develop the definition of circle using diameter and radius.

• Students know that the distance around a circle is called the circumference and discover that the ratio of the circumference to the diameter of a circle is a special number called pi, written π.

• Students know the formula for the circumference C of a circle of diameter d and radius r. They use scale models to derive these formulas.

• Students use 22/7 and 3.14 as estimates for π and informally show that is slightly greater than 3.

Relevant Vocabulary

Lesson 16 Problem Set Classwork

Opening Exercise

a. Using a compass, draw a circle like the picture to the right.

C is the center of the circle.

The distance between C and B is the radius of the circle.

b. Write your own definition for the term circle.

c. Extend segment CB to a segment AB, where A is also a point on the circle.

The length of the segment AB is called the diameter of the circle.

d. The diameter is twice, or 2 times, as long as radius.

e. Measure the radius and diameter of each circle. The center of each circle is labeled C.

f. Draw a circle of radius 6 cm.

Example 1

The ratio of the circumference to its diameter is always the same for any circle. The value of this ratio, is called the number pi and is represented by the symbol π.

Since the circumference is a little greater than 3 times the diameter, π is a number that is a little greater than 3. State:

Use the π symbol to represent this special number. Pi is a non-terminating, non-repeating decimal and mathematicians use the symbol π or approximate representations as more convenient ways to represent pi.

Example 2

a. The following circles are not drawn to scale. Find the circumference of each circle. (Use 22/7 as an approximation for π.)

b. The radius of a paper plate is 11.7 cm. Find the circumference to the nearest tenth. (Use 3.14 as an approximation for π.)

c. The radius of a paper plate is 11.7 cm. Find the circumference to the nearest hundredth. ((Use the button on your calculator as an approximation for π.)

d. A circle has a radius of r cm and a circumference of C cm. Write a formula that expresses the value of C in terms of r and π.

e. The figure below is in the shape of a semicircle. A semicircle is an arc that is "half" of a circle. Find the perimeter of the shape. (Use 3.14 for π.)

Lesson 16 Problem Set Sample Solutions

1. Find the circumference.

a. Give an exact answer in terms of π

b. Use π = 22/7 and express your answer as a fraction in lowest terms.

c. Use the π button on your calculator and express your answer to the nearest hundredth.

3. The figure shows a circle within a square. Find the circumference of the circle. Let π ≈ 3.14.

5. Find the perimeter of the semicircle. Let π ≈ 3.14.

7. Mary and Margaret are looking at a map of a running path in a local park. Which is the shorter path from E to F: along the two semicircles or along the larger semicircle? If one path is shorter, how much shorter is it?