7.2 – sectors of circles essential question: how do you find the radius of a sector given its’...
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7.2 – Sectors of Circles
Essential Question: How do you find the radius of a sector given its’ area
and arc length?
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Sector of a Circle
• the region bounded by a central angle and its intercepted arc.
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Formulas for Arc Length and Area of a Sector:
Degrees Radians
Arc Length of a Sector s = s = r θ
Area of a Sector K = K =
or K =
r2
360
2
360r
2
2
1r
sr2
1
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Example
• A sector of a circle has radius 6 cm and central angle .5 radians. Find its arc length and area.
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Example
• A sector of a circle has central angle 30° and arc length 3.5 cm. Find its area. Round to the nearest hundredth.
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Example
• A sector of a circle has area 88 cm2 and central angle 0.4 radians. Find its radius and arc length.
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Example
• A sector of a circle has perimeter 16 cm and area 15 cm2. Find all possible radii and arc lengths.
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Example
• A phonograph record with diameter 12 in. turns at 33 rpm. Find the distance that a point on the rim travels in one minute.
3
1