Understanding Sector Area

The video tutorial explains how to calculate the area of a sector using the formula involving the central angle and the radius of the circle. It provides two examples: one with a 50-degree angle and another with a 160-degree angle, demonstrating the step-by-step process of finding the sector area by applying the formula and simplifying the fractions involved.

What is the formula for calculating the area of a sector?

• Measure of the arc over 360 times pi times diameter

• Measure of the arc over 180 times pi times radius squared

• Measure of the arc over 180 times pi times diameter

• Measure of the arc over 360 times pi times radius squared

In the example with a 120° angle, what fraction of the circle's area is the sector?

• 1/2

• 1/3

• 1/6

• 1/4

For a sector with a 50° angle and radius of 5, what is the first step in finding the area?

• Find the area of the whole circle

• Divide the angle by 360

• Calculate the circumference of the circle

• Multiply the radius by the angle

What is the reduced fraction of 50/360 used in the 50° angle problem?

• 5/36

• 1/8

• 5/72

• 1/6

In the 50° angle problem, what is the final area of the sector in terms of pi?

• 125/36 pi

• 100/36 pi

• 150/36 pi

• 200/36 pi

For the 160° angle problem, what is the initial area of the circle with radius 10?

• 100 pi

• 150 pi

• 200 pi

• 50 pi

What is the reduced fraction of 160/360 used in the 160° angle problem?

• 2/3

• 5/9

• 8/9

• 4/9

What is the final area of the sector with a 160° angle in terms of pi?

• 400/9 pi

• 600/9 pi

• 300/9 pi

• 500/9 pi

Why might you use a calculator when solving these problems?

• To simplify fractions

• To find the radius

• To calculate the diameter

• To measure the angle

What is the importance of understanding the fraction of the circle in these problems?

• It determines the radius

• It helps find the diameter

• It indicates the sector's area relative to the whole circle

• It measures the circumference