Sector Area and Arc Length Problems

This video tutorial covers the calculation of the area and circumference of circles, focusing on sectors. It explains the components of a sector, such as the radius and arc, and provides formulas for calculating sector area and arc length. The tutorial includes examples and advanced problems, guiding viewers through solving for unknowns in sector-related questions. The video concludes with a summary and additional resources for further learning.

What is a sector in a circle?

• A region bounded by two radii and an arc

• The entire area of the circle

• A line segment from the center to the circumference

• A line segment connecting two points on the circle

How do you calculate the area of a sector?

• Multiply the radius by the diameter

• Multiply the circumference by the radius

• Use the formula: π * r^2

• Use the formula: (Theta/360) * π * r^2

What is the formula for calculating the arc length of a sector?

• π * diameter

• (Theta/360) * π * radius

• π * radius

• (Theta/360) * π * diameter

What is the unit of measurement for arc length?

• Square centimeters

• Centimeters

• Radians

• Degrees

If a sector has an angle of 225° and a radius of 9 cm, what is its area?

• 200.0 cm²

• 100.0 cm²

• 225.0 cm²

• 159.0 cm²

For a sector with a 225° angle and a diameter of 18 cm, what is the arc length?

• 35.3 cm

• 45.3 cm

• 25.3 cm

• 55.3 cm

How do you calculate the perimeter of a sector?

• Add the arc length to twice the radius

• Multiply the arc length by the radius

• Multiply the arc length by the diameter

• Add the arc length to the diameter

What is the simplified form of the fraction 120/360?

• 1/5

• 1/3

• 1/2

• 1/4

If the arc length of a sector is 3.5 cm and the diameter is 8 cm, what is the angle?

• 70.1°

• 60.1°

• 50.1°

• 80.1°

Given a sector area of 66 cm² and an angle of 136°, what is the radius?

• 10.5 cm

• 9.5 cm

• 8.5 cm

• 7.5 cm