Understanding Circle Geometry

The video tutorial explains how to calculate the area of a semicircle and the arc length of a partial circle. It begins by reviewing the formula for the area of a circle and applies it to find the area of a semicircle, given a radius of two. The tutorial then shifts to finding the arc length of a partial circle, which is three-fourths of the circumference, using a radius of four. The instructor provides step-by-step calculations and explanations for both problems, emphasizing the use of Pi and the relationships between radius, area, and circumference.

What is the formula for the area of a full circle?

• Pi * diameter

• 2 * Pi * radius

• Pi * radius^2

• Pi * radius

If the radius of a circle is 2, what is the area of the full circle?

• 2 Pi

• 4 Pi

• 8 Pi

• 16 Pi

How do you find the area of a semicircle from the area of a full circle?

• Multiply by 2

• Divide by 2

• Multiply by Pi

• Divide by Pi

What is the formula for the circumference of a circle?

• Pi * radius^2

• 2 * Pi * radius

• Pi * diameter

• 2 * radius

If the radius of a circle is 4, what is the circumference of the full circle?

• 4 Pi

• 12 Pi

• 16 Pi

• 8 Pi

How do you find the arc length of a partial circle?

• Multiply the circumference by the fraction of the circle

• Divide the circumference by the fraction of the circle

• Multiply the area by the fraction of the circle

• Divide the area by the fraction of the circle

What fraction of the circle is used to find the arc length in this example?

• 1/4

• 1/2

• 1/3

• 3/4

If the circumference of a circle is 8 Pi, what is 3/4 of this circumference?

• 8 Pi

• 4 Pi

• 6 Pi

• 2 Pi

What is the arc length of a partial circle that is 3/4 of the way around a circle with a circumference of 8 Pi?

• 6 Pi

• 4 Pi

• 8 Pi

• 2 Pi

How is a 90° angle related to the fraction of the circle used in this example?

• It represents the whole circle

• It represents 1/3 of the circle

• It represents 1/2 of the circle

• It represents 1/4 of the circle