Sector Area and Angle Conversion

The video tutorial explains how to calculate the area of a sector of a circle using a given radius and central angle. It covers converting degrees to radians and applying the formula for sector area. An example is provided to calculate the area of a green shaded region in a circle, which involves finding the area of a sector and subtracting the area of a triangle. The tutorial emphasizes the importance of using radians for angle measurements and demonstrates the calculations using a calculator.

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

• R x THETA

• PI x (R) SQUARED

• 1/2 x (R) SQUARED x THETA

• 1/2 x (R) x THETA

How do you convert an angle from degrees to radians?

• Multiply by 180/PI

• Divide by PI

• Multiply by PI/180

• Divide by 180

What is the approximate area of the sector with a radius of 8 feet and a central angle of 110 degrees?

• 80.3 square feet

• 61.4 square feet

• 50.2 square feet

• 70.5 square feet

In the new example, what is the radius of the circle?

• 8 centimeters

• 10 centimeters

• 12 centimeters

• 14 centimeters

What is the formula for the area of a triangle using the sine of the included angle?

• 1/2 x (A) x (B) x COTANGENT (C)

• 1/2 x (A) x (B) x TANGENT (C)

• 1/2 x (A) x (B) x COSINE (C)

• 1/2 x (A) x (B) x SINE (C)

What is the radian measure of a central angle of 80 degrees?

• 4/PI divided by 9

• 5/PI divided by 9

• 6/PI divided by 9

• 7/PI divided by 9

What is the first step in determining the area of the green shaded region?

• Calculate the area of the triangle

• Convert the angle to radians

• Calculate the area of the entire sector

• Subtract the area of the triangle from the sector

What should you ensure about the calculator when finding the area of the shaded region?

• It is in degree mode

• It is in standard mode

• It is in radian mode

• It is in scientific mode

What is the approximate area of the green shaded region?

• 27.8 square centimeters

• 25.4 square centimeters

• 31.2 square centimeters

• 29.6 square centimeters

What is the common factor used to simplify the conversion of 80 degrees to radians?

• 10

• 15

• 20

• 25