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Test your knowledge
Textbook: pp. 126–128
GoalTest Chapter III topics with multiple-choice items and problems: inscribed/circumscribed polygons, circumference, arc, radian, disc, sector and segment.
New words
radian measure · radian o‘lchovarc length · yoy uzunligisegment area · segment yuzimultiple-choice test · test
Explanation
In this lesson we use all the formulas of the chapter together. First decide what the figure is (circle, disc, sector or segment) and then choose the formula: C = 2πR, S = πR², l = πRn/180, S = πR²n/360. If the angle is given in radians, convert it by 180° = π or use l = αR directly. Before choosing a test answer, check units and whether π is left in the answer. If in doubt, estimate the size, for instance a sector's area must be smaller than that of the whole disc.
Worked examples
A regular hexagon with side 6 has a circumscribed disc with R = 6, so S = 36π.
A 60° segment of a disc of radius 6: sector 6π, triangle (equilateral, side 6) 9√3; segment = 6π − 9√3.
Class activity
“Test master”: solve three problems in a row with a classmate; for each, first say an estimate and then compare it with the exact answer.
Practice
1
How many degrees is an angle of 3π/4 radians?
135°
2
What central angle (in degrees) corresponds to an arc of length 5π in a circle of radius 5?
180°
3
What is the area of the disc inscribed in a regular hexagon with side 6?
27π
4
Why can a sector's area never exceed the area of the whole disc?
A sector is n/360 of the disc and n ≤ 360.