Relating Circumference and Area of a Circle

The video tutorial explains how to calculate the area of a circle using its circumference. It provides examples and derives formulas to understand the relationship between area, circumference, and radius. The tutorial also explores patterns in the ratio of area to circumference and demonstrates how to solve for circumference using given ratios.

What measurement is necessary to calculate the area of a circle?

• Surface area

• Diameter

• Volume

• Height

What value of pi is used in the calculations?

• 3.14159

• 3.14

• 22/7

• 3.142

How is the radius calculated from the circumference?

• Multiply circumference by pi

• Divide circumference by pi

• Multiply circumference by 2*pi

• Divide circumference by 2*pi

What is the area of a circle with a radius of approximately 9.9 inches?

• 314 square inches

• 100 square inches

• 200 square inches

• 308 square inches

What is the approximate radius of a circle with a circumference of 22 cm?

• 14 cm

• 11 cm

• 7 cm

• 3.5 cm

What is the area of a circle with a radius of 3.5 cm?

• 50 square cm

• 12.25 square cm

• 38.5 square cm

• 45 square cm

What pattern is observed in the ratio of area to circumference as the radius changes?

• It halves

• It quadruples

• It remains constant

• It doubles

What is the ratio of area to circumference for a circle with a radius of 32 cm?

• 64

• 32

• 16

• 8

How is the circumference calculated if the radius is known?

• Radius squared times pi

• Radius divided by pi

• 2 times pi times radius

• Pi times radius

What mathematical operation simplifies the ratio of area to circumference?

• Subtraction

• Division

• Multiplication

• Addition