Download presentation

Presentation is loading. Please wait.

1
Circumference and p Lesson 7.1.2

2
**Circumference and p 7.1.2 California Standards: What it means for you:**

Lesson 7.1.2 Circumference and p California Standards: Algebra and Functions 3.1 Use variables in expressions describing geometric quantities (for example, P = 2w + 2l, A = ½bh, C = pd — the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Algebra and Functions 3.2 Express in symbolic form simple relationships arising from geometry. Measurement and Geometry 1.1 Understand the concept of a constant such as p; know the formulas for the circumference and area of a circle. Measurement and Geometry 1.2 Know common estimates of p (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements. What it means for you: You’ll learn about a special number which you can use in a formula to find the circumference of a circle. Key words: circumference diameter radius pi (p) estimate

3
Lesson 7.1.2 Circumference and p In this Lesson, you’ll learn about the distance around the outside of a circle, which is called the circumference. There is a clever way to work out the circumference if you know the radius or diameter of the circle, and it involves a special number.

4
Lesson 7.1.2 Circumference and p The Circumference is Another Important Measurement The distance around the edge of a circle is called the circumference. Imagine that a circle is like a loop of string. If you cut the string and laid it out flat, you could measure the length of the string. If you could cut a circle and lay it out in the same way, the length you measured would be the circumference.

5
Lesson 7.1.2 Circumference and p Example 1 Norman is walking around the edge of a large, circular rug. By the time he is one-third of the way around it, he has walked 8 feet. What is the circumference of the rug? Solution The circumference is the distance all the way around the rug. Norman has walked one-third of the way around, so the circumference is 3 times the distance he has walked. 3 × 8 = 24 The circumference of the rug is 24 feet. Solution follows…

6
**Circumference and p 7.1.2 Guided Practice**

Lesson 7.1.2 Circumference and p Guided Practice 1. Jack is running around a circular track. When he is halfway around, he has run 150 yards. What is the circumference of the track? 150 yd × 2 = 300 yd 2. Judy’s scarf is 60 cm long. The scarf will go around a telephone pole exactly 3 times. What is the circumference of the pole? 60 cm ÷ 3 = 20 cm 3. Jorge is riding his bicycle. When he travels 5 m, his front wheel goes around 5 times. What is the circumference of the wheel? 5 m ÷ 5 = 1 m Solution follows…

7
**Circumference and p 7.1.2 Circumference Is Related to Diameter**

Lesson 7.1.2 Circumference and p Circumference Is Related to Diameter You’ve seen that the diameter is always twice the radius. Diameter and circumference are related too — the circumference of a circle is always just over three times its diameter. The diameter of this circle is 1. If the diameter is doubled, the circumference also doubles. 3.14 1 Its circumference is about 3.14.

8
Lesson 7.1.2 Circumference and p In fact, circumference ÷ diameter for any circle is always … This number is very important in math. The full version of it is a never-ending decimal. There’s a special symbol mathematicians use instead of writing out the full number. The symbol is a Greek letter called pi (pronounced “pie”). It looks like this: p p is kind of tricky — it’s a symbol, so it looks like a variable. This is one time where a symbol doesn’t stand for an unknown. It’s just the name of a special number.

9
**Circumference and p 7.1.2 C = pd C = 2pr**

Lesson 7.1.2 Circumference and p You Can Use p in a Formula to Find Circumference Using C for circumference and d for diameter, you can use p to make a formula for the circumference of a circle: C = pd This formula is often written using r for radius, like this: C = 2pr

10
Lesson 7.1.2 Circumference and p Example 2 A circle has a diameter of 12 inches. What is its exact circumference? Solution You can use the formula C = pd to solve this question. C = p × 12 = 12p in. You can leave p in an exact answer, because it is a number. Solution follows…

11
**Circumference and p 7.1.2 Guided Practice**

Lesson 7.1.2 Circumference and p Guided Practice In Exercises 4–9, find the exact circumference of a circle with the given diameter or radius. Remember: C = pd 4. d = 20 in d = 13 ft. 6. d = 3.5 m 7. r = 5 ft. 8. r = 26 cm 9. r = 6.3 cm 20p in. 13p ft 3.5p m 10p ft 52p cm 12.6p cm Solution follows…

12
**Circumference and p 7.1.2 You Can Often Use a Rounded Value of p**

Lesson 7.1.2 Circumference and p You Can Often Use a Rounded Value of p If an exercise asks you to give the exact circumference, you should always leave p in the answer. Numbers with p in them are not very easy to work with, so it is more usual to estimate the circumference using a rounded value of p. If the radius or diameter is given as a decimal, you should use 3.14 or as the value of p. 22 7 If the question uses fractions, you should use You should normally use a rounded value of p in real-life situations.

13
Lesson 7.1.2 Circumference and p Example 3 Alicia has a circular swimming pool. The diameter of the pool is 30 ft. What is the circumference of Alicia’s pool? Solution Using the formula C = pd, and estimating p as 3.14, you can solve the question: C = 3.14 × 30 = 94.2 The circumference of Alicia’s pool is 94.2 ft. Solution follows…

14
Lesson 7.1.2 Circumference and p Example 4 T.J. is cutting a circle of paper to use on a poster for a math project. The circle has a radius of 3 in. What is its circumference? 1 4 Solution 22 7 You can use the formula C = 2pr, and estimate p as : C = 2 × × 3 22 7 1 4 = 2 × × 22 7 13 4 = = 572 28 143 7 3 7 = 20 So the circumference of the circle is in. 3 7 Solution follows…

15
**Circumference and p 7.1.2 Guided Practice**

Lesson 7.1.2 Circumference and p Guided Practice In Exercises 10–15, calculate the circumference of a circle with the given diameter or radius. Use p = 3.14. 10. d = 15 cm r = 11 yd 12. d = 42 in r = 6 m 14. d = 9.2 ft r = 13.5 m C = pd = 3.14 × 15 = 47.1 cm C = 2pr = 2 × 3.14 × 11 = 69.1 yd C = pd = 3.14 × 42 = in. C = 2pr = 2 × 3.14 × 6 = 37.7 m C = pd = 3.14 × 9.2 = 28.9 ft C = 2pr = 2 × 3.14 × 13.5 = 84.8 m Solution follows…

16
**Circumference and p 7.1.2 Guided Practice**

Lesson 7.1.2 Circumference and p Guided Practice In Exercises 16–21, calculate the circumference of a circle with the given diameter or radius. Use p = . 22 7 16. r = yd d = m 18. r = in r = m 20. d = ft d = ft 1 3 5 8 C = 2pr = 2 × × 1 3 = yd 2 21 22 7 C = pd = × 5 8 = m 27 28 22 7 4 11 3 7 C = 2pr = 2 × × 4 11 = in 2 7 22 C = 2pr = 2 × × 12 3 7 = m 6 49 22 1 9 5 17 C = pd = × 9 1 9 = ft 40 63 22 7 C = pd = × 1 5 17 = ft 119 8 22 7 Solution follows…

17
**Circumference and p 7.1.2 Independent Practice**

Lesson 7.1.2 Circumference and p Independent Practice In Exercises 1–9, use a suitable estimate of p to find the circumference of a circle with the given diameter or radius. 1. r = ft r = 2.75 cm 3. d = 6.3 m d = 13 in. 5. r = m d = 0.75 yd 7. r = 3.3 ft d = m 9. r = 8.1 in. 5 6 5 ft 5 21 17.3 cm 19.8 m 40.8 in. 7 11 4 m 2.4 yd 4 3 4 m 4 21 20.7 ft 50.9 in. Solution follows…

18
**Circumference and p 7.1.2 Independent Practice**

Lesson 7.1.2 Circumference and p Independent Practice 10. Complete the sentence by filling in the blanks. p is the ratio of a circle’s c _ _ _ _ _ _ _ _ _ _ _ _ to its d _ _ _ _ _ _ _. ircumference iameter 11. A good estimate of the height of an elephant from its foot to its shoulder is twice the circumference of its (roughly circular) foot. A zoologist in Africa finds an elephant footprint with a 12-inch diameter. Estimate how tall the elephant that left the footprint is. About 75 in. Solution follows…

19
**Circumference and p 7.1.2 Round Up**

Lesson 7.1.2 Circumference and p Round Up p is a really useful and important number. It might look a little strange, but remember, it is just a fixed number. You will see p again many times in math, including in the next Lesson of this book.

Similar presentations

Presentation is loading. Please wait....

OK

Completing the Square Topic 7.2.1.

Completing the Square Topic 7.2.1.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on biography of mahatma gandhi Ppt on famous temples of india in hindi Ppt on any state of india Ppt on indian politics and culture Ppt online compressor training Ppt on testing of circuit breaker Ppt on sbi life insurance Ppt on tamper resistant electrical outlets Ppt on condition monitoring vibration Ppt on statistics and probability tutorial