12-6 6 th grade math

12-66th grade math

Area of a Circle

Objective

• To find areas of circles

• Why? To know how to use formulas and evaluate variable expressions using the order of operations. To further your knowledge of geometry and measurement.

California State Standards MG 1.1 : Understand the concept of a constant, such as Π (pi); know the formulas for the circumference … of a

circle.MG 1.2: know common estimates of Π (pi) (3.14, 22/7) and

use these values to estimate and calculated the circumference … of circles; compare with actual measurements

AF 3.1: Use variables in expressions describing geometric quantities … (e.g., C = Π x d or C = Π x r: ½ the formula(s) for … the area of a circle …)

AF 3.2: Express in symbolic form simple relationships arising from geometry.

MR 2.2: Apply strategies and results from simpler problems to more complex problems.

Vocabulary • Area

– The square units needed to fill in a circle. Pi = Π. Its value is ≈ 3.14 or 22 .

7 • A = Π x r x r • C = Π x r²

• Pi = 3.14 or 22/7. Use the decimal or fraction value of pi that

best accommodates the computation of the problem.Radius– ½ line segment of a circle

Diameter– Line segment across a circle

How to Remember the Formula: Area of a Circle

1) A circle is round (duh). So remember a circle uses pi (pie), 3.14 or 22/7

2) Look at the word: ‘area’– The word area has 2 a’s to stand for the ²– The word area has an ‘r’ to stand for the radius. Remember the

story Sir Cumference? Radius was short and had short reach.– The word RADIUS = 3 syllables. The word AREA = 3 syllables.

3) Therefore the formula =A = 3.14 x r² (3.14 x r x r)

How to Find the Area of a Circle1) Observe or draw the

circle figure. Be sure the radius or diameter is labeled.

2) Write out the formula: 3.14 x r x r

3) Be sure to use the radius and square it (times itself).

4) Check work and add label² to answer.

A.

7 ft

A = 3.14 x 7 x 7= 153.86 ft²≈ 154 ft²

B. 12

A = 3.14 x 6 x 6= 113.04≈ 113

Try It!Find the area of each circle. Round to the

nearest whole number.

1) R = 1.4 cm2) R = 2 cm3) D = 64) R = 1.9 ft

1) R = 1.4 cm3.14 x 1.4 x 1.4= 6.1544≈ 6 cm²

2) R = 2 cm3.14 x 2 x 2= 12.56 cm≈ 13 cm²

3) D = 6 yd3.14 x 3 x 3= 28.26≈ 28 yd²

4) R = 1.9 ft3.14 x (1.9 x 1.9= 11.3354≈ 11 ft²

Try One More!5) Find the area of the shaded region.

7

7 5 7 7

5) (3.14 x 3.5 x 3.5) ½ + (7 x 5)= (38.465) ½ + 35≈ 19 + 35≈ 54 square units

Objective Review • To find areas of circles

• Why? You now know how to use formulas and evaluate variable expressions using the order of operations. You have furthered your knowledge of geometry and measurement.

• The area of any circle can be found by multiplying pi and the square of the radius.

Independent Practice

• Complete problems 6-12

• Copy original problem first.

• Show all work!

• If time, complete Mixed Review: 13-19

• If still more time, work on Accelerated Math.