Area and Properties of Circles

Mrs. Apia presents lessons 17 and 18, focusing on the area and circumference of circles. Students learn to derive the formula for the area of a circle by rearranging circle segments into a rectangle. The lessons cover solving problems involving semicircles, quarter circles, and composite shapes. Key concepts include the relationship between circle and rectangle areas, and using pi approximations for calculations.

What is the main focus of Lesson 17?

• Learning about the volume of a sphere

• Exploring the properties of triangles

• Studying the angles in a polygon

• Understanding the relationship between circumference and area of a circle

How is the area of a circle derived in the lesson?

• By cutting the circle into triangle wedges and forming a rectangle

• By using the Pythagorean theorem

• By transforming a circle into a square

• By measuring the diameter directly

What is the formula for the area of a circle?

• r²/2

• 2πr

• πd

• πr²

In the sprinkler example, what is the radius of the circular region?

• 15 feet

• 12 feet

• 10 feet

• 6 feet

How is the area of a semicircle calculated?

• 2πr

• πd

• 1/2 × πr²

• πr²

What approximation is used for π in the semicircle example?

• 3.14

• 22/7

• 3.14159

• 3.2

What is the area of a quarter circle with radius 6 cm?

• 36π cm²

• 18π cm²

• 9π cm²

• 27π cm²

What is the formula for the area of a quarter circle?

• 1/4 × πr²

• πr²

• 2πr

• 1/2 × πr²

What is emphasized in the summary regarding problem-solving?

• Using decimals for all calculations

• Avoiding the use of fractions

• Relying solely on calculators

• Simplifying computations using fraction arithmetic

What is the relationship between the area of a semicircle and a full circle?

• A semicircle has the same area as a full circle

• A semicircle has twice the area of a full circle

• A semicircle has one-fourth the area of a full circle

• A semicircle has half the area of a full circle