10.2.2 Circles I, PT3 Focus Practice


Question 6:
In the diagram below, CD is an arc of a circle with centre O.


Determine the area of the shaded region.
( Use π= 22 7 )

Solution:

Area of sector=Area of circle× 72 o 360 o                       = 22 7 × ( 10 ) 2 × 72 o 360 o                       = 440 7  cm 2 Area of ΔOBD= 1 2 ×6×8                        =24  cm 2 Area of shaded region= 440 7 24                                   =38 6 7  cm 2


Question 7:
In diagram below, ABC is a semicircle with centre O.

Calculate the area, in cm2 , of the shaded region.
( Use π= 22 7 )

Solution:
ACB= 90 o AB= 6 2 + 8 2     = 100     =10 cm Radius=10÷2            =5 cm The shaded region =( 1 2 × 22 7 ×5×5 )( 1 2 ×6×8 ) =39 2 7 24 =15 2 7  cm 2

Question 8:
In diagram below, ABC is an arc of a circle centre O

The radius of the circle is 14 cm and AD = 2 DE.
Calculate the perimeter, in cm, of the whole diagram.
( Use π= 22 7 )

Solution:
Length of arc ABC = 3 4 ×2πr = 3 4 ×2× 22 7 ×14 =66 cm Perimeter of the whole diagram =16+8+8+66 =98 cm

Question 9:
In diagram below, KLMN is a square and KLON is a quadrant of a circle with centre K.



Calculate the area, in cm2, of the coloured region.
( Use π= 22 7 )

Solution:
Area of the coloured region = 45 o 360 o ×π r 2 = 45 o 360 o × 22 7 × 14 2 =77  cm 2


Question 10:
Diagram below shows two quadrants, AOC and EOD with centre O.



Sector AOB and sector BOC have the same area.
Calculate the area, in cm2, of the coloured region.
( Use π= 22 7 )

Solution:
Area of the sector AOB=Area of the sector BOC Therefore, AOB=BOC                             = 90 o ÷2                             = 45 o Area of the coloured region = 45 o 360 o × 22 7 × 16 2 =100 4 7  cm 2

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