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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Presentation transcript:

7.2 – Sectors of Circles Essential Question: How do you find the radius of a sector given its’ area and arc length?

Sector of a Circle the region bounded by a central angle and its intercepted arc.

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 =

Example A sector of a circle has radius 6 cm and central angle .5 radians. Find its arc length and area.

Example A sector of a circle has central angle 30° and arc length 3.5 cm. Find its area. Round to the nearest hundredth.

Example A sector of a circle has area 88 cm2 and central angle 0.4 radians. Find its radius and arc length.

Example A sector of a circle has perimeter 16 cm and area 15 cm2. Find all possible radii and arc lengths.

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.