Circles, Prisms and Solids

Arcs and sectors as fractions of a circle, and the volumes and surface areas of the solids built from circles and polygons.

หลักสูตรแกนกลาง / สสวท.: การวัดและเรขาคณิต (Geometry and Measure)ตรงกับ ม.3 บทที่ 7 วงกลม และบทที่ 8 พีระมิด กรวย และทรงกลม
Common Core (US): 7.G, G-GMD
Cambridge: Lower Secondary Stage 9 — Geometry and Measure: shapes and measurements

10.1 Arcs and sectors

A fraction of the whole circle

arc = \frac{θ}{360} \times 2 π r sector area = \frac{θ}{360} \times π r^{2}

Neither is a new formula — both are the circle formulae multiplied by the fraction of the turn the sector occupies.

ตัวอย่าง

A sector has radius $10$ cm and angle $7 2^{\circ}$ . Find its arc length and area.

วิธีทำ

1. $\frac{72}{360} = \frac{1}{5}$ of the circle
2.Arc: $\frac{1}{5} \times 2 π \times 10 = 4 π \approx 12.57$ cm
3.Area: $\frac{1}{5} \times π \times 100 = 20 π \approx 62.83$ cm²

ตอบ Arc about $12.6$ cm, area about $62.8$ cm²

ข้อควรระวัง

The PERIMETER of a sector is the arc plus the two straight radii. Quoting the arc alone answers a different question, and it is the same trap as the semicircle in Stage 8.

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