Year 10 Surface Area and Volume 1 - Dobmaths

7.5 cm

4 cm

A

6 cm

B

102.92 cm310 cm 4009.33 cm3

8 10 cTmhe volume of thitcisrmoessss-ppseehcrpteieornnedailcaiusrleaarclosest to:

height.

A

1563 m3

8.3 cm C 1336.4 cm3

7.2 m B 391 m3

Year 10 Mathematics a Volume

D 64b6.7Voclmum3 e

= lengt1h2?.4brcemadth ? height = area of base ? height

C 4690 m3 D 217 m3

= lbh

Surface A=rer2a? hand Volume Practice Test 1

4

T=he7v.5olcumm?e cl=os1e8s0t ctmo:3

6ofctmhi?s

4sqcumare

pyram=id i?s 5 = 250

? 5 ? 10

Nam9e___T_he_v_o_lu_m_e__of_t_hi_s_s_w_im_m__in_g_p_o_ol_i_s

A 450.6=c7m835.4 cm3

closest to:

6 1 FFininddthtehevosluumrfeacoef a1thr5ee.3afocolmlfotwhBCiengfo14sl37olol5.i9wd14s.i9.ncmgcm3so3lids

aa)

Db 143.82 cmb)3

9.4 cm

2m

8 m

c 3 m

20 m

1.2 m

7m

A 576 m3

B 336 m3

5

The volume of this cone is closest to:

8m

6 cm

A 20 927 cm3

C 672 m36 cm

D 32.2 m3

2 3

dFind the surface correct to 1 d.p.

6Fcomr the cylinder

4a1re.3a comf aBCceyl82in86d86e24rc5, mwc3mhi3ch given finDd 6976 cm3

has

a1r0adiuTcfslhooesfes8ustrcfmtaoc:aenadreaahoefitghhist ocflo9s.e5dccmylinder A 2178 cm2 B 15c3m6.17 cm2

is

(i) the curved sur1f2accemarea 12 cm

20 cm

32 cm C 160 850 cm2

7 cm

16 cm

(ii) the area o2f5t.4hecmcircular ends

g

h

8 cm

Surface Area and Volume (DChap6te5r385) Scymlla2bus reference i

(iii) the s7ucrmface area

40 cm

14 cm

5 cm

Give the answe3rcsmcorrect to 2 d.p 11 The s1u3rcfmace area of this open cylind1e2rcims 12 A cylinder has a curved surface

4 Find the curved surfcalcoeseasrteatoo:f the cylinder correct to 1 decimal place400 cm21a5ncdmradius of 9.2 cm. T

A 170 m2

20 cmis closest to:

j

11 cm

k

20 cm

5.3 m 13 cm

B 57 m2

C 143 m2 D 71.6 m2 8 cm

A 20.8 cm C 23 122 cm

B 6.9 cm D 43.4 cm

13 cm

20 cm

4.3 m 25 cm

5 A water tank is cylindrical in shape. If it has a 1.5 m radius and a height of 2 m, find the area of the sheIef tyomuehtaalvneeaendyeddiftfioccuoltnyswtriuthctthite. s(Ae qnuswesetirocnosr,rreecftetroto2 tdh.ep)examples and questions in the listed in the table.

6 A swimming pool is shown in the diagram. Find the cost of tiling the walls and floor of

the pool at $85 Qpueresmti2on

1?3

4?7

8

9

10

Section

8.8Am

B

C

D

1Am . UNITS, AREA AND VOL2 mUME REVIEW

This section reviews parts of Stage 4 in preparation for this chapter.

8.9 m

4.6 m

Area Conversions

base unit is m2

100 mm2 = 1 cm2

2

2

ab

cb

4 cm

2m

6 cm

10 cm

77m Calcula7te.5tchme areas of the following figures

10 cm

Volume = cross-sectional area times perpendicular

height.

a)

6 cm

b)

6 cm

c)

a Volume

b Volume

e = length ? breadth ? heightf = area of base ? height

= lbh

= r2 ? h

12 cm

= 7.5 cm ? 6 cm ? 4 cm

= 180 cm3

12 cm

20 cm

= ? 5 ? 5 ? 10

= 250 = 785.4 cm3

1 cm

16 cm

8 Find the volume of the following solids

6 m

3 cm

Finhd aa)

the

vol8umcme

of

the

following

b 5 cm

isbol)ids.

13 cm

2m 7m

12 cm

8m

6 cm

14 cm 20 cm

c

c)

15 cm

6 cm

9

Fkind d

t2h0e

cvmolumes

of

the

cylinders e

below.

Give

the

answers f

to

1

d.p

a)

13 cm

8 cm

b)

20 cm 6 cm

25 cm12 cm

12 cm

20 cm

7 cm

16 cm

1 cm

g

h

8 cm

i

10 Find the7vcomlume of a rectangular pyramid which has a base 6.2 cm l1o4ncgmand 4.5 cm

wide and a he3igchmt of 9.3 cm.

5 cm

11 A pyramid as a hexagon1a3lcbmase with an area of 12.6 cm122.cImf the height of the pyramid

is 7.1 cm. Calculate the volume

15 cm

20 cm

12j Calculated the volume ofkthese pyramids

20 cm

a) 11 cm

b)

13 cm

8 cm

13 cm

20 cm

25 cm

13 Find the volume of a cone with a radius of 6.2 cm and a height of 5.8 cm. Give your answer correct to 3 significant figures

14 Use Pythagoras' Theorem to calculate the height h correct to 3 decimal places and then use this value to calculate the volume correct to 3 significant figures

15 Find the volume of a sphere with a radius of 5.2 cm. Give your answer to 3 sig figs 16 If the diameter of a sphere is 3.6 m, calculate the volume of the sphere correct to

1 decimal place 17 Calculate the volume of these solids

18 A swimming pool is shown. Calculate the volume of the pool in cubic metres and its capacity in litres . 1 m2 = 1000 litres

19 A tin is cylindrical in shape. Calculate the volume of the tin in cubic centimetres to 2 d.p and its capacity to the nearest litre if the tin has a height of 45 cm and a diameter of 25 cm.

ANSWERS

1 a) 172 m2

b) 96 m2

2 879.6 cm2

3 i) 80 424.77 cm2 ii) 2513.28 cm2 iii) 82 938.05 cm2

4 143.2 m2 5 32.99 m2 6 4.6 + 9.2 + 40.94 + 13.2 + 13.2 = 81.14 m2 7 a) 80 cm2

81.14 x 85 = $6896.90

8 a) 112 m3

b) 3060 cm3 c) 42 cm3

9 a) 1539.4 cm3 b) 904.8 cm3

10 86.49 cm3

11 29.82 cm3

12 a) 48 m3

b) 40 m3

13 233 cm3

14 h = 8.307 Volume = 869.9 cm3

15 589 cm3

16 24.4 m3

17 a) 50.4 + 17.64 = 68.04 m3 b) 315 + 173.18 = 488.18 cm3

18 Volume = 200 m3 Capacity = 200 x 1000 = 200 000 litres

19 Volume = 22 089.32 cm3 Capacity = 22 litres

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