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P6 MATHS
© Singapore Asia Publishers Pte LtdWebsite: www.sapgrp.com | Facebook: Singapore-Asia-Publishers
SAPMATP6_W30Page 1/6
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
© Singapore Asia Publishers Pte LtdWebsite: www.sapgrp.com | Facebook: Singapore-Asia-Publishers
Solutions to Circles
SAPMATP6_W30Page 2/6
Taken from Learning Maths Book 6B
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
© Singapore Asia Publishers Pte LtdWebsite: www.sapgrp.com | Facebook: Singapore-Asia-Publishers
SAPMATP6_W30Page 3/6
Taken from Learning Maths Book 6B
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
© Singapore Asia Publishers Pte LtdWebsite: www.sapgrp.com | Facebook: Singapore-Asia-Publishers
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
SAPMATP6_W30Page 4/6
Taken from Learning Maths Book 6B
P6 MATHS
© Singapore Asia Publishers Pte LtdWebsite: www.sapgrp.com | Facebook: Singapore-Asia-Publishers
SAPMATP6_W30Page 5/6
Taken from Learning Maths Book 6B
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
© Singapore Asia Publishers Pte LtdWebsite: www.sapgrp.com | Facebook: Singapore-Asia-Publishers
SAPMATP6_W30Page 6/6
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