Cambridge International Mathematics

250 Mensuration (solids and containers) (Chapter 11)

Example 15 Self Tutor

A concrete tank has an external diameter

of 10 m and an internal height of 3 m. If

the walls and bottom of the tank are 30 cm

thick, how many cubic metres of concrete

are required to make the tank?

The tank’s walls form a hollow cylinder with outer radius 5 m and inner radius 4 : 7 m.

Its bottom is a cylinder with radius 5 m and height 30 cm.

walls of tank: volume=base area£height

=[¼£ 52 ¡¼£(4:7)^2 ]£ 3

¼ 27 : 43 m^3

bottom of tank: volume=base area£height

=¼£ 52 £ 0 : 3

¼ 23 : 56 m^3

Total volume of concrete required¼(27:43 + 23:56)m^3 ¼ 51 : 0 m^3.

EXERCISE 11E

2 A castle is surrounded by a circular moat which is 5 m wide

and 2 m deep. The diameter of the outer edge of the moat is

50 m. Find, in kilolitres, the quantity of water in the moat.

3aFind the volume of the dumbbell illustrated.

b If the material used to make the dumbbell weighs 2 : 523

grams per cm^3 , find the total mass of the dumbbell.

3m

30 cm

30 cm

10 m

h

r

50 m

5m

5cm 13 cm

16 cm

6cm

1 An observatory is built as a cylinder with a hemisphere above it.

a Suppose r=4m and h=5m. Find to 3 significant

figures, the observatory’s:

i above ground surface area

ii volume.

b Suppose h=2r.

i Find a formula for the volume of the solid in simplest form.

ii If the volume is 1944 ¼, findr.

iii If the surface area is 384 ¼, findr.

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