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Homework Practice

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Areas Related to Circles Practice 1: Circumference, Arcs and Sectors

Section A: Core Ideas

Question 1mcq
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 2mcq
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
Question 3mcq
Find the area of a sector of radius 77 cm and angle 60∘60^\circ using π=227\pi=\frac{22}{7}.
A.77 cm277\text{ cm}^2
B.1543 cm2\frac{154}{3}\text{ cm}^2
C.44 cm244\text{ cm}^2
D.773 cm2\frac{77}{3}\text{ cm}^2
Question 4mcq
A sector has radius 77 cm and arc length 1111 cm. What is its perimeter?
A.7777 cm
B.1414 cm
C.2525 cm
D.1818 cm
Question 5mcq
The region between a chord and its corresponding minor arc is called:
A.Diameter
B.Minor segment
C.Sector
D.Semicircle

Section B: Apply and Check

Question 6mcq
For radius 66 cm and central angle 60∘60^\circ, which expression gives the minor segment area?
A.60360π(6)2−34(6)2\frac{60}{360}\pi(6)^2-\frac{\sqrt3}{4}(6)^2
B.π(6)2+36\pi(6)^2+36
C.2π(6)−62\pi(6)-6
D.90360π(6)2−18\frac{90}{360}\pi(6)^2-18
Question 7mcq
For radius 1010 cm and central angle 90∘90^\circ, the segment area equals:
A.100π−50 cm2100\pi-50\text{ cm}^2
B.25π+50 cm225\pi+50\text{ cm}^2
C.50π−25 cm250\pi-25\text{ cm}^2
D.25π−50 cm225\pi-50\text{ cm}^2
Question 8mcq
For a 120∘120^\circ sector, which idea is used to find the minor segment area?
A.Use only circumference
B.Ignore the central angle
C.Subtract the triangle formed by the two radii and chord from the sector area
D.Add the triangle to the sector
Question 9mcq
A shaded design is made of a rectangle plus a semicircle on one side. How should its area be found?
A.Area of rectangle minus full circle
B.Area of rectangle plus area of semicircle
C.Only area of full circle
D.Perimeter of rectangle plus arc
Question 10mcq
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.20+7π20+7\pi
B.20+14π20+14\pi
C.10+49π10+49\pi
D.20+49π20+49\pi