Circumference and Diameter Relationships

The video tutorial covers problem-solving techniques related to calculating the circumference of circles. It begins with an introduction to the concept using the United States Capitol Rotunda as an example. The tutorial then moves on to calculate the circumference of a clock using its minute hand and a barbecue pit for a rotisserie. It explains the proportional relationship between the diameter and circumference of circles, using examples like the Earth and Moon to illustrate these concepts. The tutorial emphasizes the importance of understanding the formulas and calculations involved in determining circumference.

What is the formula used to calculate the circumference of a circle when the radius is known?

• C = πr^2

• C = r/2

• C = 2πr

• C = πD

If the radius of a clock's minute hand is 5.25 inches, what is the circumference of the clock?

• 6.28 inches

• 10.5 inches

• 32.97 inches

• 16.5 inches

Given a circular barbecue pit with a circumference of 9 feet, how do you find the diameter?

• Multiply the circumference by π

• Subtract π from the circumference

• Add π to the circumference

• Divide the circumference by π

What is the relationship between the circumference and diameter of a circle?

• The ratio of circumference to diameter is π

• They are equal

• The diameter is three times the circumference

• The circumference is twice the diameter

How is the proportionality between circumference and diameter expressed mathematically?

• C = D/π

• C = 2D

• C/D = π

• C = D

What is the radius of the Earth used in the comparison with the Moon?

• 1,737 kilometers

• 6,371 kilometers

• 3,959 kilometers

• 12,742 kilometers

How do you calculate the circumference of the Earth given its radius?

• C = 2πr

• C = πr^2

• C = r/2

• C = πD

What is the approximate circumference of the Earth based on the given radius?

• 80,000 kilometers

• 40,000 kilometers

• 20,000 kilometers

• 60,000 kilometers

What is the radius of the Moon used in the comparison with the Earth?

• 1,737 kilometers

• 12,742 kilometers

• 6,371 kilometers

• 3,959 kilometers

How do you form a ratio to compare the circumferences of the Earth and the Moon?

• Earth radius divided by Moon radius

• Moon circumference divided by Earth circumference

• Earth circumference divided by Moon circumference

• Moon radius divided by Earth radius