Circles - SAP Education

P6 MATHS

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Taken from Learning Maths Book 6B

Circles

Do these word problems. Show your working clearly in the space provided.

1. Thefigurebelowshowsafieldthatismadeupofarectangleandtwoidenticalsemicircles.

(Takeπ= 22___ 7 )

(a) Whatistheareaofthefield?

(b) IfAnnarunsroundthefieldfor8times,howfardoessherun?

100m

70m

2. The figurebelow ismadeupof two identical large semicircles and three identical smallsemicircles.Oisthecentreofthelargesemicircle.Findthelengthofthepieceofwireneededtoformthisfigure.(Takeπ=3.14)

18cm

O

P6 MATHS


Solutions to Circles



1. (a) Areaoftherectangle=L×B=100×70=7000m2

Areaofeachsemicircle= �r2___ 2 = 22___ 7 × 70___ 2 × 70___ 2 × 1__ 2 =1925m2

7000+1925+1925=10850m2

The area of the field is 10 850 m2.

(b) Circumferenceofeachsemicircle= �d___ 2 = 22___ 7 ×70× 1__ 2 =110m110+100+110+100=420mThe perimeter of the field is 420 m.8×420=3360mSheruns3360 m.

2. Circumferenceofeachlargesemicircle= �d___ 2 = 3.14×18_________ 2 =28.26cm

Circumferenceofeachsmallsemicircle= �d___ 2 = 3.14×(18÷2)

______________ 2 =14.13cm

14.13+28.26+14.13+28.26+14.13+9+9=116.91cmThe length of the piece of wire needed to form this figure is 116.91 cm.

P6 MATHS




Circles

Do these word problems. Show your working clearly in the space provided.

1. Thefigurebelowshowseightidenticalquadrantsenclosedinasquare.Every2quadrants

overlapeachother,formingashadedportion.Findtheareaoftheshadedportioninthe

figure.(Takeπ= 22___ 7 )

42cm

2. Fouridenticalquadrantsareplacedinsideasquareofside60cm.Findtheperimeteroftheshadedpart.(Takeπ=3.14)

60cm

3. Thefigurebelowismadeofatriangleandtwosemicircles.Thesidesofthetriangleis12cm,

16cmand20cmrespectively.Findtheareaofthefigure.(Takeπ= 22___ 7 )

12cm

16c

m

20cm

P6 MATHS


1. Radiusofeachquadrant=42÷2=21cm

Areaofeachquadrant= �r2___ 4 = 22___ 7 ×21×21× 1__ 4 =346.5cm2

Areaofaquarterofthesquare= 1__ 4 ×42×42=441cm2

Areaofeachunshadedareainaquarter-square=441–346.5=94.5cm2

Areaoftheshadedareainaquarterofthesquare=441–94.5–94.5=252cm2

4×252=1008cm2

The area of the shaded portion in the figure is 1008 cm2.

2. Radiusofeachquadrant=60÷2=30cm

Circumferenceofeachquadrant= 2�r___ 4 = 2×3.14×30_____________ 4 =47.1cm

4×47.1=188.4cmTheperimeteroftheshadedpartis188.4 cm.

3. Areaofthetriangle= 1__ 2 ×B×H= 1__ 2 ×12×16=96cm2

Areaofthebiggersemicircle= �r2___ 2 = 22___ 7 × 20___ 2 × 20___ 2 × 1__ 2 =157 1__ 7 cm2

Areaofthesmallersemicircle= �r2___ 2 = 22___ 7 × 16___ 2 × 16___ 2 × 1__ 2 =100 4__ 7 cm2

96+157 1__ 7 +100 4__ 7 =353 5__ 7 cm2

The area of the figure is 353 5 __ 7 cm2.

Solutions to Circles



P6 MATHS




Pie Charts

The pie chart shows the different types of books Gisele read in a certain month.

Self-enrichmentbooks

Mysterybooks

1__3

Motivationalbooks

1. Whatfractionofthebooksweremysterybooks?

2. IfGiseleread12motivationalbooksthatmonth,howmanybooksdidshereadinall?

3. Howmanyself-enrichmentbooksdidGiselereadthatmonth?

1.1 __4 2.36 books

1 __3 → 12

3 __3 → 3 × 12 = 36

3.15 self-enrichment books

1 __4×36=9mysterybooks

36–12–9=15

Solutions:

P6 MATHS



Taken from Mental Mathematics Book 6

Mental Maths: Finding the Sum of Unusual Numbers (Part 1)

STRATEGY

Findthesumof5,10,20,40and80.

Step1:80+80=160 [addthelargestnumbertwice]Step2:160–5=155 [subtractthesmallestnumberfromtheresultobtainedinstep1]

5+10+20+40+80=155

Notethatthisstrategyworksifeachnumberintheseriesistwiceofitsprecedingnumber.

Do these sums mentally.

1. 8+16+32+64+128=

2. 11+22+44+88+176=

3. 15+30+60+120+240=

4. 20+40+80+160+320=

5. 25+50+100+200+400=

6. 33+66+132+264+528=

7. 45+90+180+360+720=

8. 50+100+200+400+800=

9. 55+110+220+440+880=

10. 75+150+300+600+1200=

Solutions:1.2482.3413.4654.6205.7756.10237.13958.15509.170510.2325

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Circles - SAP Education