03-10-2025-Area of Sector Lesson

Draw

Solve this riddle.

Draw

Draw two straight lines through the box to end up with four sections, each containing three of each symbol.

● I can define the parts of a circle
● I can define and measure in a circle
● I can find the measure of segments of a circle
● I can discover the properties of tangent lines
● I can find the measure of angles inside and outside of a circle
● I can find missing measures of angles and arcs using circle theorems.
● I can find the length of an arc and area of a sector of a circle.

● I can explain radian angle measures in terms of a circular radius and
arc length

Objectives

I can calculate lengths of arcs and areas of sectors in circles.

​Learning Target

Circle Vocab

​The measure of an arc is the degree of the angle that intercepts the arc. Remember that the measure of an arc is a degree, not a distance.
https://study.com/academy/lesson/measure-of-an-arc.html

​https://study.com/academy/lesson/measure-of-an-arc.html

​Arc length is literally the length of the arc of a portion of a circle.
This arc is a part of the total circumference of a circle.
This length is measured as a linear distance.

https://study.com/academy/lesson/arc-length-definition-equation.html

Draw

A runner completes a 60° section of a circular track with a 40-meter radius. How far do they run?

Show your process.

Draw

A runner completes a 45° section of a circular track with a 50-meter radius. How far do they run?

Show your process.

Draw

A Ferris wheel has a radius of 25 meters. A rider moves along a 90° arc. Find the arc length.

Solution:

Show your process.

Draw

A highway curve follows a 45° arc of a 200-meter radius. Find the arc length.

Show your process.

Draw

A bike tire has a radius of 14 inches. It rolls along a 30° arc. Find the arc length.

Show your process

Draw

A swing ride moves along a 75° arc with a radius of 18 feet. Find the arc length.

Show your process

Draw

A satellite dish has a radius of 15 meters and receives signals from a 60° sector. Find the arc length.

Show your process.

Sector

The region inside a circle lying between two radii of the circle.

​Circumference for linear distance

Area of Circle for Area of Sector

​Question: Where do we see sectors in real life?

• Examples:

  1. Pizza Slices 🍕 – The crust length is the arc, and the slice area is the sector.

  2. Ferris Wheel Ride 🎡 – A Ferris wheel seat moves along an arc, and the space covered is a sector.

  3. Highway Curves 🛣 – Roads designed with circular turns use sector area for construction planning.

​https://study.com/academy/lesson/finding-the-area-of-a-sector-formula-practice-problems.html

​

​https://study.com/learn/lesson/sector-circle-overview-formula.html

Math Response

Find the area of the sector.

Round to the nearest hundredth.

Type answer here

Correct Answer: 28.26

Deg^°

Rad

Math Response

Find the area of the sector. Round to the nearest hundredth.

Type answer here

Correct Answer: 22.06

Deg^°

Rad

Draw

A pizza has a radius of 10 inches. One slice has a central angle of 45°. What is the area of that slice?

Show your process.

Draw

A Ferris wheel has a radius of 20 meters. A rider moves along a 90° sector. Find the area of the sector.

Show your process.

Draw

A sprinkler sprays water in a 120° sector over a circular garden with a 6-meter radius. Find the area covered by water.

Show your process.

Draw

A curved road section follows a 135° sector with a radius of 50 meters. Find the area of the road section.

Show your process.

Draw

A survey pie chart has a 72° sector representing one category. If the radius is 8 cm, find the area of the sector.

Show your process

Draw

A wind turbine blade moves through a 60° sector with a radius of 30 meters. Find the area swept by the blade.

Show your process

Draw

A pivot irrigation system covers a 270° sector of a circular field with a 20-meter radius. Find the area of the irrigated land.

Show your process.

Draw

A spotlight illuminates a 120° sector on a stage with a radius of 5 meters. Find the lit area.

Show the process.

Draw

A park has a circular flower bed with a 75° sector. The radius is 10 m. Find the area.

Show your process.

Poll

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