Cambridge International Mathematics

r

h

10 cm

12 cm 8cm

semi-circular

b

2 a^2 x

x

xm

xm

2 xm

q°

Mensuration (solids and containers) (Chapter 11) 251

5 For the given solid, calculate the:

a surface area

b volume

c mass given a density of 6 : 7 g per cm^3.

6 Assuming these solids have a density ofdg per cm^3 , find formulae for their:

i surface areaA ii volumeV iii massM.

ab

7 A large grain container is built as a cone over a cylinder.

a Find the capacity of the container in terms ofx.

b If the capacity of the container is 500 kl, findxcorrect to 4

significant figures.

c State, in terms ofx, the surface area of the container. Do not

forget the base.

d The cone is made from a sector of a circle with sector angleμo.

Find the value ofμto the nearest degree.

8 Regulation army huts have the dimensions shown. They sleep

36 soldiers. Each soldier must have access to 11 m^3 of air

space.

a Find the internal volume of air space.

b Hence, find the dimensions of the hut.

c If each bed and surrounds requires 4 m^2 of floor space,

can the 36 soldiers be accommodated? How can this be achieved?

4aConsider the icecream cone opposite, filled with icecream:

Suppose r=3: 3 cm and h=10: 5 cm. Find, correct to 3

significant figures, the:

i surface area ii volume of the icecream.

b Suppose r=2: 9 cm and the volume is 130 cm^3. Findh.

c Suppose h=3r and the volume is 115 cm^3. Findr.

d Supposer=4: 5 cm and the total surface area of the cone and

icecream is 320 cm^2. Find the slant length of the cone.

am^2 am

2

am

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_11\251IGCSE01_11.CDR Tuesday, 14 October 2008 2:59:26 PM PETER