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Areas Related to Circles Final Assessment

Core Concepts

Question 1mcq
In a second review item, the region between a chord and its corresponding minor arc is called:
A.Sector
B.Semicircle
C.Diameter
D.Minor segment
Question 2mcq
In a second review item, for radius 66 cm and central angle 60∘60^\circ, which expression gives the minor segment area?
A.2π(6)−62\pi(6)-6
B.90360π(6)2−18\frac{90}{360}\pi(6)^2-18
C.60360π(6)2−34(6)2\frac{60}{360}\pi(6)^2-\frac{\sqrt3}{4}(6)^2
D.π(6)2+36\pi(6)^2+36
Question 3mcq
In a second review item, for radius 1010 cm and central angle 90∘90^\circ, the segment area equals:
A.50π−25 cm250\pi-25\text{ cm}^2
B.25π−50 cm225\pi-50\text{ cm}^2
C.100π−50 cm2100\pi-50\text{ cm}^2
D.25π+50 cm225\pi+50\text{ cm}^2
Question 4mcq
In a second review item, for a 120∘120^\circ sector, which idea is used to find the minor segment area?
A.Subtract the triangle formed by the two radii and chord from the sector area
B.Add the triangle to the sector
C.Use only circumference
D.Ignore the central angle
Question 5mcq
In a second review item, a shaded design is made of a rectangle plus a semicircle on one side. How should its area be found?
A.Only area of full circle
B.Perimeter of rectangle plus arc
C.Area of rectangle minus full circle
D.Area of rectangle plus area of semicircle
Question 6mcq
In a second review item, the boundary of a shape includes two straight sides of 1010 cm each and a semicircular arc of radius 77 cm. What expression gives its perimeter?
A.10+49π10+49\pi
B.20+49π20+49\pi
C.20+7π20+7\pi
D.20+14π20+14\pi

Skill Practice

Question 7mcq
In a second review item, a circular park of radius 2121 m has a 120∘120^\circ sector used for flowers. What fraction of the park is used?
A.14\frac{1}{4}
B.13\frac{1}{3}
C.12\frac{1}{2}
D.23\frac{2}{3}
Question 8mcq
In a second review item, which value of π\pi is usually convenient when the radius is 1414 cm?
A.227\frac{22}{7}
B.33
C.2\sqrt2
D.1010
Question 9mcq
In a second review item, a student finds sector area when the question asks for arc length. What is the mistake?
A.They used the right value of π\pi
B.They correctly found perimeter
C.They found a length in square units
D.They confused a region measure with a boundary length
Question 10mcq
In a second review item, find the area of a circle of radius 77 cm using π=227\pi=\frac{22}{7}.
A.49 cm249\text{ cm}^2
B.22 cm222\text{ cm}^2
C.154 cm2154\text{ cm}^2
D.44 cm244\text{ cm}^2
Question 11mcq
Find the arc length for radius 77 cm and central angle 120∘120^\circ using π=227\pi=\frac{22}{7}.
A.120120 cm
B.443\frac{44}{3} cm
C.77 cm
D.1414 cm
Question 12mcq
Find the sector area for radius 77 cm and angle 180∘180^\circ using π=227\pi=\frac{22}{7}.
A.77 cm277\text{ cm}^2
B.7777 cm
C.49 cm249\text{ cm}^2
D.14 cm214\text{ cm}^2

Application and Reasoning

Question 13mcq
In a second review item, which approach best matches the skill: find perimeter of a sector?
A.Use circle area for every question
B.Use circumference for every shaded region
C.Ignore whether the answer needs square units
D.Identify the required region or boundary first, then apply the matching circle formula.
Question 14mcq
In a second review item, which approach best matches the skill: understand minor and major segments?
A.Use circumference for every shaded region
B.Ignore whether the answer needs square units
C.Identify the required region or boundary first, then apply the matching circle formula.
D.Use circle area for every question
Question 15mcq
In a second review item, which approach best matches the skill: find area of segment for 60°?
A.Ignore whether the answer needs square units
B.Identify the required region or boundary first, then apply the matching circle formula.
C.Use circle area for every question
D.Use circumference for every shaded region
Question 16mcq
In a second review item, which approach best matches the skill: find area of segment for 90°?
A.Identify the required region or boundary first, then apply the matching circle formula.
B.Use circle area for every question
C.Use circumference for every shaded region
D.Ignore whether the answer needs square units
Question 17mcq
In a second review item, which approach best matches the skill: find area of segment for 120°?
A.Use circle area for every question
B.Use circumference for every shaded region
C.Ignore whether the answer needs square units
D.Identify the required region or boundary first, then apply the matching circle formula.
Question 18mcq
In a second review item, which approach best matches the skill: find area of combined circular figures?
A.Use circumference for every shaded region
B.Ignore whether the answer needs square units
C.Identify the required region or boundary first, then apply the matching circle formula.
D.Use circle area for every question

Mixed Challenge

Question 19mcq
In a second review item, which approach best matches the skill: find perimeter of circular plane figures?
A.Ignore whether the answer needs square units
B.Identify the required region or boundary first, then apply the matching circle formula.
C.Use circle area for every question
D.Use circumference for every shaded region
Question 20mcq
In a second review item, which approach best matches the skill: solve real-life area problems involving circles?
A.Identify the required region or boundary first, then apply the matching circle formula.
B.Use circle area for every question
C.Use circumference for every shaded region
D.Ignore whether the answer needs square units
Question 21mcq
In a second review item, which approach best matches the skill: use π approximations appropriately?
A.Use circle area for every question
B.Use circumference for every shaded region
C.Ignore whether the answer needs square units
D.Identify the required region or boundary first, then apply the matching circle formula.
Question 22mcq
In a second review item, which approach best matches the skill: avoid confusing arc, sector and segment?
A.Use circumference for every shaded region
B.Ignore whether the answer needs square units
C.Identify the required region or boundary first, then apply the matching circle formula.
D.Use circle area for every question
Question 23mcq
In a second review item, find the circumference of a circle of radius 77 cm using π=227\pi=\frac{22}{7}.
A.4949 cm
B.4444 cm
C.154154 cm
D.2222 cm
Question 24mcq
In a second review item, find the length of an arc of a circle with radius 1414 cm and central angle 90∘90^\circ.
A.2222 cm
B.4444 cm
C.1111 cm
D.8888 cm