Circle Geometry and Measurements

The lesson covers the relationship between area and circumference, using transformations of circles into parallelograms and triangles to derive formulas. It includes practical examples like estimating the area of a circular field and tiling a circular table. The session concludes with practice problems to reinforce the concepts.

What is the area of a square with side length 800 meters?

• 640,000 square meters

• 800,000 square meters

• 1,600,000 square meters

• 400,000 square meters

When rearranging a circle into a parallelogram, what represents the base of the parallelogram?

• The diameter of the circle

• The radius of the circle

• Half of the circumference

• The full circumference

In the circle to triangle transformation, what does the height of the triangle represent?

• Half of the circumference

• The full circumference

• The radius of the circle

• The diameter of the circle

If a circular table has a diameter of 28 inches, what is its radius?

• 14 inches

• 56 inches

• 7 inches

• 28 inches

What is the formula for the area of a circle?

• πd

• πr²

• 2πd

• 2πr

If the circumference of a circle is 76 cm, what is the approximate diameter?

• 12 cm

• 76 cm

• 38 cm

• 24 cm

How much farther does May travel than Kieran if May rides on a ring 8 feet further out?

• 8 feet

• 50 feet

• 17 feet

• 9 feet

What is the speed of May if she travels 105 feet in 12 seconds?

• 4.6 feet per second

• 8.75 feet per second

• 7.5 feet per second

• 9 feet per second

Which coin has a diameter of approximately 2.10 cm?

• Penny

• Nickel

• Dime

• Quarter

How many rotations does a dime make if it rolls 41.8 cm?

• 10 rotations

• 7.4 rotations

• 5 rotations

• 3 rotations