12-6 6th 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 ½ r: 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 Pi Radius Diameter 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 Circle 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 Observe or draw the circle figure. Be sure the radius or diameter is labeled. 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.

Try It! R = 1.4 cm 3.14 x 1.4 x 1.4 = 6.1544 ≈ 6 cm² 2) R = 2 cm 3) D = 6 yd 3.14 x 3 x 3 = 28.26 ≈ 28 yd² 4) R = 1.9 ft 3.14 x (1.9 x 1.9 = 11.3354 ≈ 11 ft² Try It! Find the area of each circle. Round to the nearest whole number. R = 1.4 cm R = 2 cm D = 6 R = 1.9 ft

Try One More! Find the area of the shaded region. 7 7 5 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.