CCSS HSG-C.B.5 Worksheets
Geometry · Circles
Derive by similarity that arc length is proportional to the radius, defining radian measure as the constant of proportionality, and derive the formula for the area of a sector.
Below are free printable worksheets that support HSG-C.B.5. Print them as PDFs, or generate a fresh one. Every math answer key is computed in code, so it is never wrong.
Teaching guide
What students learn
Derive by similarity that arc length is proportional to the radius, defining radian measure as the constant of proportionality, and derive the formula for the area of a sector.
Worked example
A sector of a circle has radius 36 cm and angle 30°. Find the arc length, (a) exactly in terms of pi, and (b) rounded to 1 decimal place.
Answer: (a) 6π cm (b) 18.8 cm
Why: Arc length = (theta/360) x 2πr = (30360) x 2π(36) = (30360) x 72π = 6π cm. As a decimal: 6 x π ≈ 18.8 cm.
Generated and checked in code, so it is correct.
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