AREA OF CIRCLES

MG 1.1 Understand the concept of a constant such as π; know the formulas for the circumference and area of a circle. Objective: Understand how the area formula for circles is related to the area formula for parallelograms Learning target: Answer at least 3 of the 4 area of a circle questions correctly on the exit ticket.

What is the formula for area of a parallelogram? How can we turn a circle into a parallelogram? Area of a parallelogram = base × height

Area of circle parallelogram = base × height Area of circle parallelogram = πr × r Area of circle parallelogram = π × r²

What is the formula for the area of a circle? Area of a circle = π×radius² Remember, the exponent of 2 means to multiply the radius by itself, NOT by the number 2. 5² = 5×5 = 25, NOT 5×2

What is the area of this circle? Area = π × radius² A = π × (4 m)² A = π × 4 m × 4 m A = 16π meters²

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What is the area of this circle? Area = π × radius² A = π × (3 ft)² A = π × 3 ft × 3 ft A = 9π ft²

What is the area of this circle? Area = π × radius² A = π × (6 in)² A = π × 6 in × 6 in A = 36π in²

What is the area of this circle? Use 3.14 for π. Area = π × radius² A = π × (1 km)² A = π × 1 km × 1 km A = 1π km² A = 1 × 3.14 km² A = 3.14 km²

How do we find the area of a circle when we only know the diameter? Divide the diameter by 2 to find the length of the radius. Use the same formula as before: Area = π × radius²

What is the area of this circle? Diameter = 14 cm Radius = 14÷2 = 7 cm Area = π × radius² A = π × (7 cm )² A = π × 7 cm × 7 cm A = 49π cm²

What is the area of this circle? Diameter = 22 yd Radius = 22 ÷ 2 = 11 yd Area = π × radius² A = π × (11 yd)² A = π × 11 yd × 11 yd A = 121π yd²

What is the area of this circle? Use 3.14 for π. Diameter = 6 m Radius = 6 ÷ 2 = 3 m Area = π × radius² A = π × (3 m)² A = π × 3 m × 3 m A = 9π m² A = 9 ×3.14 m² A = m²

Direct Station We will use the whiteboards to practice area of circle problems.

Collaborative Station: Fill in the Table For each circle, one piece of information will be given to you: either the circle’s radius, diameter, circumference, or area. Work with your partner to fill in the other 3 pieces of information Example: RadiusDiameterCircumferenceArea Circle 14 cm 8 cm 8π cm = cm 16π cm² = cm²

Independent Station Continue ST Math’s unit on area and perimeter