Exploring the Area of a Circle in 7th Grade Math

This video tutorial explores the area and circumference of circles through various problems and examples. It begins with an analysis of graphs showing relationships between diameter, radius, circumference, and area. The tutorial then moves on to estimating circle areas using squares and calculating the area of a larger circle based on a given circle's dimensions. It also includes solving problems related to the circumference of circles, using real-world examples like bike wheels. The video concludes with a call to action for viewers to engage with the content.

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

• Pi

• One

• One-half

• Two

If the diameter of a circle is doubled, by what factor does the area increase?

• Two

• Four

• Eight

• Sixteen

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

• Proportional with a constant of Pi

• Proportional with a constant of One-half

• Not proportional

• Proportional with a constant of One

Why is the area of a circle less than the area of the circumscribed square?

• Because the circle fits perfectly inside the square

• Because the circle is smaller than the square

• Because the square covers areas outside the circle

• Because the circle is larger than the square

What is the area of the smaller square inside the circle in problem 2b?

• 12 square units

• 24 square units

• 36 square units

• 18 square units

How much larger is the area of Circle B compared to Circle A?

• Three times

• Twelve times

• Nine times

• Six times

What is the circumference of Lynn's bike wheels?

• 1.82 meters

• 2.00 meters

• 1.50 meters

• 2.82 meters

Calculate the circumference of a circle with a diameter of 15 centimeters.

• 45 centimeters

• 47 centimeters

• 42 centimeters

• 50 centimeters

What is the diameter of Priya's circle?

• 9.96 centimeters

• 6.96 centimeters

• 8.96 centimeters

• 7.96 centimeters

What is the circumference of Claire's circle?

• 55 centimeters

• 65 centimeters

• 85 centimeters

• 75 centimeters