Curriculum / Math / 10th Grade / Unit 7: Circles / Lesson 13
Math
Unit 7
10th Grade
Lesson 13 of 14
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Calculate the sector area of a circle. Identify relationships between sector area, arc angle, and radius.
The core standards covered in this lesson
G.C.B.5 — Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
The foundational standards covered in this lesson
7.G.B.4 — Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
What is the area of the shaded region shown below where circle $$A$$ has a radius of $$\overline{AB}$$ measuring $$4$$ units?
If you would like to eat the most pizza, which coupon should you use?
Pizza Doubler by Dan Meyer is licensed under the CC BY 3.0 license. Accessed June 13, 2017, 12:16 p.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Circle $$A$$ and circle $$C$$ are shown below.
Geometry - 8.13 TT by Match Fishtank is made available by GeoGebra under the CC BY-NC-SA 3.0 license. Copyright © International GeoGebra Institute, 2013. Accessed June 13, 2017, 12:24 p.m..
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 12
Lesson 14
Topic A: Equations of Circles
Derive the equation of a circle using the Pythagorean Theorem where the center of the circle is at the origin.
G.GPE.A.1 G.GPE.B.4
Given a circle with a center translated from the origin, write the equation of the circle and describe its features.
G.C.A.1 G.CO.A.5 G.GPE.A.1
Write an equation for a circle in standard form by completing the square. Describe the transformations of a circle.
G.CO.A.5 G.GPE.A.1
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Topic B: Angle and Segment Relationships in Inscribed and Circumscribed Figures
Define a chord to derive the Chord Central Angles Conjecture and Thales’ Theorem.
G.C.A.2
Describe the relationship between inscribed and central angles in terms of their intercepted arc.
Determine the angle and length relationships between intersecting chords.
Prove properties of angles in a quadrilateral inscribed in a circle.
G.C.A.3
Define and determine properties of tangents and secants of circles to solve problems with inscribed and circumscribed triangles.
G.C.A.2 G.C.A.3
Construct tangent lines to a circle to define and describe the circumscribed angle.
G.C.A.2 G.C.A.4
Use angle and side length relationships with chords, tangents, inscribed angles, and circumscribed angles to solve problems.
Topic C: Arc Length, Radians, and Sector Area
Define, describe, and calculate arc length.
G.C.B.5
Describe the proportional relationship between arc length and the radius of a circle. Convert between degrees and radians to write the arc measure in radians.
Use sector area of circles to calculate the composite area of figures.
G.C.B.5 N.Q.A.2 N.Q.A.3
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