Exploring Circles: Algebra of Circumference and Area

This video tutorial covers the concepts of circumference and area of circles. It explains the relationship between circumference and diameter, introducing Pi as a constant ratio. The tutorial provides examples of calculating circumference using both approximate and exact values of Pi. It also covers the formula for the area of a circle, demonstrating calculations with examples. The video concludes with practical applications, solving real-world problems involving circular measurements.

What is the ratio of a circle's circumference to its diameter?

• π/2

• 2π

• Pi (π)

• π^2

If the diameter of a circle is 9 inches, what is the approximate circumference using 3.14 for Pi?

• 18.8 inches

• 201.0 inches

• 28.3 inches

• 45.2 inches

How can the exact circumference of a circle be represented?

• Pi times diameter

• 2 times radius

• Radius squared

• 3.14 times diameter

What is the circumference of a circle with a radius of 7.2 cm?

• 201.0 cm

• 45.2 cm

• 28.3 cm

• 18.8 cm

What formula is used to calculate the area of a circle?

• Pi times radius squared

• Pi times diameter

• 2 times Pi times radius

• Radius squared divided by 2

If the radius of a circle is 8 km, what is the approximate area?

• 201.0 km²

• 176.6 km²

• 379.9 km²

• 19.5 km²

What is the exact area of a circle with a radius of 8 km?

• 201π km²

• 28π km²

• 45π km²

• 64π km²

How do you find the diameter of a circle if you know its circumference?

• Divide the circumference by Pi

• Multiply the circumference by Pi

• Square the circumference and divide by Pi

• Divide the circumference by 2

What is the first step in solving for the radius if you know the area of a circle?

• Take the square root of the area

• Square the area

• Multiply the area by Pi

• Divide the area by Pi

If a circular area rug covers 19.5 square feet, what is the approximate diameter?

• 19.5 feet

• 5 feet

• 10 feet

• 2.5 feet