Circle and Sector Area Concepts

The video tutorial covers the basic concepts of circles and sectors, including definitions of key terms such as center, diameter, radius, central angle, and sector. It explains how to calculate the area of a circle using the formula A = πr² and the area of a sector using the formula A = (x/360)πr². The tutorial includes several example problems to demonstrate these calculations in practice, emphasizing rounding to the nearest tenth or hundredth as required.

What is the definition of a circle?

• A shape with four equal sides

• A set of points equidistant from a center point

• A line segment with two endpoints

• A polygon with three sides

What is a diameter?

• A line segment that is tangent to the circle

• A line segment that passes through the center and has endpoints on the circle

• A line segment from the center to a point on the circle

• A line segment that does not touch the circle

How is a radius defined?

• A line segment from the center to a point on the circle

• A line segment that passes through the center and has endpoints on the circle

• A line segment that is tangent to the circle

• A line segment that is outside the circle

What is a central angle?

• An angle whose vertex is on the circle

• An angle that is tangent to the circle

• An angle that is outside the circle

• An angle whose vertex is the center of the circle

What distinguishes a minor sector from a major sector?

• A major sector is smaller than a minor sector

• A major sector has an arc measure less than 180 degrees

• A minor sector has an arc measure less than 180 degrees

• A minor sector has an arc measure greater than 180 degrees

How do you calculate the area of a circle?

• Area = pi times diameter squared

• Area = pi times radius squared

• Area = 2 times pi times radius

• Area = pi times radius

What is the formula for the area of a sector?

• Area = (central angle/360) times pi times radius squared

• Area = pi times diameter squared

• Area = 2 times pi times radius

• Area = pi times radius

In the example problem, what is the area of a circle with a radius of 5.7 feet?

• 118.8 square feet

• 32.49 square feet

• 221.7 square feet

• 102.1 square feet

How do you find the radius if the diameter is given?

• Square the diameter

• Subtract the diameter from the circumference

• Multiply the diameter by 2

• Divide the diameter by 2

What is the approximate area of a major sector with a central angle of 332 degrees and a radius of 12.6 yards?

• 36.3 square yards

• 22.2 square yards

• 459.97 square yards

• 38.79 square yards