AREA OF CIRCLES. MG 1.1 Understand the concept of a constant such as π; know the formulas for the...

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AREA OF CIRCLES

Transcript of AREA OF CIRCLES. MG 1.1 Understand the concept of a constant such as π; know the formulas for the...

Page 1: 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.

AREA OF CIRCLES

Page 2: 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.

• 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.

Page 3: 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.

• What is the formula for area of a parallelogram?

• How can we turn a circle into a parallelogram?

• Area of a parallelogram = base × height

Page 4: 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.

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

Page 5: 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.

• 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

Page 6: 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.

• What is the area of this circle?

• Area = π × radius²• A = π × (4 m)²• A = π × 4 m × 4 m• A = 16π meters²

Page 7: 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.

Answering using iPads• Open up Safari in your iPad• Go to www.m.socrative.com• For the Room Number, type in: MrPMath• Click “Join Room”• Wait for more instructions!

Page 8: 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.

• What is the area of this circle?

• Area = π × radius²• A = π × (3 ft)²• A = π × 3 ft × 3 ft• A = 9π ft²

Page 9: 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.

• What is the area of this circle?

• Area = π × radius²• A = π × (6 in)²• A = π × 6 in × 6 in• A = 36π in²

Page 10: 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.

• 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

Page 11: 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 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

Page 12: 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.

• 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

Page 13: 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.

• 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

Page 14: 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.

• 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 = 28.26 m²

Page 15: 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.

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

problems.

Page 16: 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.

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:Radius Diameter Circumference Area

Circle 1 4 cm8 cm 8π cm =

25.12 cm16π cm² = 50.24 cm²

Page 17: 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.

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