Circle Measurements and Ratios

Mrs. Groovy Groves guides students through various geometry problems, focusing on calculating areas of circles and complex shapes, understanding proportional relationships, and applying these concepts to real-world scenarios. The lesson includes step-by-step instructions for finding the area of a folded circle, shaded regions, and complex shapes, as well as exploring proportional relationships in geometry and reading rates.

If a circle with a diameter of 12 inches is folded in half twice, what is the area of the resulting shape?

• 18π square inches

• 28 square inches

• 9π square inches

• 36π square inches

What is the area of a rectangle with a base of 18 inches and a height of 30 inches?

• 540 square inches

• 600 square inches

• 360 square inches

• 480 square inches

How do you calculate the area of a circle if the circumference is given as 63 inches?

• Use the formula A = πr²

• Use the formula A = πd

• Use the formula A = 2πr

• Use the formula A = πc

Which of the following pairs of circle measurements are proportional?

• Radius and Area

• Diameter and Area

• Diameter and Circumference

• Radius and Diameter

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

• 4

• 2

• 1/2

• π

If the radius of a circle is doubled, how does the circumference change?

• It triples

• It doubles

• It quadruples

• It remains the same

If the diameter of a circle is 10, what is the circumference?

• 15π

• 5π

• 20π

• 10π

Elena reads 4 pages while Jada reads 5 pages. What is the ratio of Jada's reading speed to Elena's?

• 4:5

• 5:4

• 1:1

• 2:3

If Jada reads 15 pages, how many pages does Elena read at the same rate?

• 20 pages

• 12 pages

• 15 pages

• 18 pages

What equation represents the relationship between Elena's and Jada's reading rates?

• E = 5/4 J

• J = 4/5 E

• E = 4/5 J

• J = 5/4 E