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Lesson 7-2 Sectors of Circles

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Objective:

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To find the arc length and area of a sector of a circle and to solve problems involving apparent size.

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A sector of a circle is the piece of pizza/pie that is cut out of a circular pizza/pie.

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Suppose we have a sector like the one shown: 12 60° s

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Suppose we have a sector like the one shown: When working with formulas involving sectors; r, s and θ are the variables involved. θ must always be in terms of radians to be used appropriately. 12 60° s

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Suppose we have a sector like the one shown: Therefore, before you attempt to find s, r, or the area of a sector; first convert θ to radian measure if it is not already done so. 12 60° s

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To change a degree measure to a radian measure, multiply by

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So, if the angle measure given is 60 0 ; we first convert by multiplying

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Now to find the area of a sector, we can simply use the formula:

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A sector of a circle has arc length 6 cm and area 75 cm 2. Find its radius and the measure of its central angle.

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When there is nothing in our field of vision against which to judge the size of an object, we perceive the object to be smaller when it is farther away. For example, the sun is much larger than the moon, but we perceive the sun to be about the same size as the moon because the sun is so much farther from Earth.

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So, how big an object looks depends not only on its size but also on the angle that it subtends at our eyes.

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The measure of this angle is called the object’s apparent size.

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Jupiter has an apparent size of 0.01° when it is 8 x 10 8 km from Earth. Find the approximate diameter of Jupiter.

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A sector has perimeter 16 cm and area 15 cm 2. Find its radius r and arc length s.

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Assignment: Pg. 265 C.E. 1-4 all W.E. 1-15 odd

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