Circle Geometry and Proportionality Concepts

This lesson covers the application of the area of circles, focusing on calculating areas of shapes made up of circles. It includes activities on using pi in calculations, comparing shaded regions, and an optional activity on calculating the area of a running track. The lesson concludes with homework problems and a summary of key concepts.

What does it mean to leave an answer in terms of Pi?

• To express the answer with the symbol Pi instead of a numerical value

• To use 22/7 as the value of Pi

• To use 3.14 as the value of Pi

• To round the answer to the nearest whole number

In Activity 1, what is the radius of the field if the side length of the square is 800 meters?

• 800 meters

• 400 meters

• 1600 meters

• 200 meters

Which value of Pi provides a more precise area calculation?

• 3.14

• 3.1

• 22/7

• Pi button on the calculator

In Activity 2, what is the area of a square with side length 12 units?

• 36 square units

• 24 square units

• 12 square units

• 144 square units

How many smaller circles are equivalent to one large circle in terms of area in Activity 2?

• Two

• Three

• Nine

• Four

What is the first step in calculating the area of the running track in Activity 3?

• Calculate the area of the grass field

• Find the area of the straight sections

• Measure the width of the lanes

• Determine the perimeter of the track

In the running track problem, what is the radius of the small circle?

• 46.2 meters

• 92.52 meters

• 73 meters

• 36.5 meters

When folding a circle with a 12-inch diameter in half twice, what fraction of the original circle remains?

• 1/3

• 1/8

• 1/4

• 1/2

What is the constant of proportionality between the radius and diameter of a circle?

• 2

• Pi

• 3.14

• 1/2

If Jada reads 5 pages for every 4 pages Elena reads, what is the ratio of Jada's reading speed to Elena's?

• 5:4

• 1:1

• 4:5

• 2:1