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Buite-oppervlakte en volume : antwoorde

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Surface area and volume : answers

Ant. / Ans. 1.1

BO / SA = 2lb + 2(l + b)h
= 2 x 4 x 8 + 2(4 + 8) x 5 cm2
= 64 + 120 cm2
= 184 cm2

Vol = lbh
= 4 x 8 x 5 cm3
= 160 cm3

Vr. / Qu. 1.1

Ant. / Ans. 1.2

BO / SA = 2πr2 + 2πrh
= 2 x π x 112 + 2 x π x 11 x 12 mm2
= 760,2654 + 829,3804 mm2
= 1 589,65 mm2

Vol = πr2h
= π x 112 x 12 mm3
= 4 561,59 mm3

Vr. / Qu. 1.2

Ant. / Ans. 1.3

BO / SA = 6 x s2
= 6 x 82 m2
= 384 m2

Vol = s3
= 83 m3
= 512 m3

Vr. / Qu. 1.3

Ant. / Ans. 1.4

BO / SA = 2πr2 + 2πrh
= 2 x π x 212 + 2 x π x 21 x 14 cm2
= 2 770,88472.. + 1 847,25648.. cm2
= 4 618,14 cm2

Vol = πr2h
= π x 212 x 14 cm3
= 19 396,19 cm3

Vr. / Qu. 1.4

Ant. / Ans. 1.5

BO prisma = 2 x opperv. driehoek + omtrek x lengte van prisma
= bh + (s1 + s2 + s3)l
Vol = opperv. van driehoekige basis x lengte  =  (1/2)bhl
Ant. / Ans. 1.5

SA prism = 2 x area of triangle + perimeter of triangle x length
= bh + (s1 + s2 + s3)l
Vol = area of triangular base x length  =  (1/2)bhl

BO prisma / SA prism = bh + (s1 + s2 + s3)l
= 24 x 12 + (18 + 18 + 24) x 20 cm2
= 288 + 1 200 cm2
= 1 488 cm2

Vol = (1/2)bhl
= (1/2) x 24 x 12 x 20 3 cm3
= 2 880 cm3

Vr. / Qu. 1.5

2.1   nuwe mates / new measurements: l = 16 cm, b = 8 cm,
h = 10 cm
BO / SA = 2bh + 2(b + h)l
= 2 x 8 x 10 + 2(8 + 10) x 16 cm2
= 736 cm2

Vol = lbh
= 16 x 8 x 10 cm3
= 1 280 cm3

2.2   Ou BO / Original SA = 184 cm2 en / and
Nuwe BO / New SA = 736 cm2.
Verandering / Change = 736 ÷ 184    = 4

Ou / Original Volume = 160 cm3 en / and
Nuwe / New Volume = 1 280 cm3.
Verandering / Change = 1 280 ÷ 116    = 8

3.1   BO kubus / SA cube = 6s2
6s2 = 150
s = √(150 ÷ 6)
= 5
sy / side = 5 cm

3.2   Vol kubus / cube = s3
= 53 cm3
= 125 cm3

4.1   Volume silinder / cylinder = πr2h
πr2 x 18 = 1 413
r = √(1 413 ÷ 18 × π)
= 5
radius = 5 mm en / and
middellyn / diamter is 10 mm.

4.2   BO silinder/SA cylinder = 2πr2 + 2πrh
= 2 x π x 52 + 2 x π x 5 x 18 mm2
= 722,57 mm2

BO / SA = 4πr2
= 4 x π x 52 cm2
= 314,16 cm2

OF / OR
BO / SA = 4π(d ÷ 2)2
= πd2
= π102 cm2
= 314,16 cm2

Volume = (4 ÷ 3)πr3
= (4/3) x π x 53 cm3
= 523,60 cm3

6.1   BO / SA = πr2 + πrh
= π x 62 + π x 6 x 30 cm2
= 678,58 cm2

6.2   Volume = (1 ÷ 3)πr2h
= (1/3) x π x 62 x 8 cm3
= 301,59 cm3

7.1   BO / SA = 4πr2
∴  4 x π x r2  =  1 257
r2   = 1 257 ÷ 4 π
= 100
r  = 10 dm

7.2   Volume = (4 ÷ 3)πr3
= (4/3) x π x 103 dm3
= 4 188,79 dm3

8.1   BO / SA = πr2 + πrh
= π x 62 + π x 6 x 15 mm2
= 395,84 mm2

6.2   Volume = (1 ÷ 3)πr2h
= (1/3) x π x 62 x 9 mm3
= 339,29 mm3

Volume van keël /
Volume of cone = (1/3) x πr2 x h
= (1/3) x π x (6/2)2 x 6 cm3
= 56,55 cm3

Volume roomys /
ice cream = (4 ÷ 3)πr3
= (4/3) x π x 33 cm3
= 113,10 cm3

Die volume van die roomys is dubbel die kapasiteit van die horing en kan dus nie in die
horing inpas nie.
The volume of the ice crean is double the capacity of the cone and cannot be contained in the cone.

Vraag / Question 9

 volume volume 8 ──────────── = ──────────── = ─── buite-oppervlakte surface area 3

∴   3 × Volume  =  8 × BO / SA

3 × (4 ÷ 3) × π × r3  =  8 × 4 × π × r3

4 × π × r3  =  32 × π × r3

r  =  8    . . . ÷  met / by  4 × π × r2

BO / SA  = 4 x π x r2
= 4 x π x 82
= 804,25 eenhede/units2

Volume  = (4 ÷ 3) x π x r3
= (4/3) x π x 83
= 2 144,66 eenhede/units3

lengte van bak = lengte van plaat − 2 x breedte van omgevoude stuk
= 150 − 2 x 5  =  140 cm
breedte van bak = breedte van plaat − 2 x breedte van omgevoude stuk
= 65 − 2 x 5  =  55 cm
length of basin = length of sheet − 2 x width of upturned piece
= 150 − 2 x 5  =  140 cm
= 65 − 2 x 5  =  55 cm
volume = lbh
= 140 x 55 x 5 cm3
= 38 500 cm3
= 38 500 ÷ 1 000 l     . . . 1 000 cm3 = 1 l
= 38,5 l

r = 1,5 ÷ 2 = 0,75

 1 4 1 Volume = ── ( ── π r3) + π r2 h + ─ π r2 h 2 3 3

 2 1 = ── × π 0,753 + π × 0,752 × 2 + ─ × π × 0,752 × 0,25  m3 3 3

= 4,565 m3

Oppervlakte halwe sfeer / Area of half a sphere = (1/2) x 4 π r2  = 2 π r2
= 2 × π × 0,752  m2
= 3,53429... m2

Oppervlakte silinder / Area of cylinder = 4 π r h
= 2 × π × 0,75 × 2  m2
= 9,42477... m2

Oppervlakte keël / Area of cone = π r skuinshoogte / slanting height
= π × 0,75 × 0,79  m2
= 1,86139... m2

Totale buite-oppervlakte / Total surface area = 3,53429 + 9,42477 + 1,86139 m2
= 14,82 m2

Vraag / Question 12