HSC Worked Solutions
07
(i)
(ii)
(iii)
23
b
projectmaths.com.au
A cylindrical water
tank, of height 2 m, is
placed in the ground at
a school. The radius of
the tank is
3.78 metres. The hole
is 2 metres deep. When
the tank is placed in
the hole there is a gap
of 1 metre all the way around the side of the tank.
(i)
When digging the hole for the water tank, what volume of soil was removed?
Give your answer to the nearest cubic metre.
(ii)
Sprinklers are used to water the school oval at a rate of 7500 litres per hour.
The water tank holds 90 000 litres when full. For how many hours can the
sprinklers be used before a full tank is emptied?
(iii)
Water is to be collected in the tank from the roof of the school hall, which has
an area of 400 m2. During a storm, 20 mm of rain falls on the roof and is
collected in the tank. How many litres of water were collected?
Volume =
=
=
=
r2h
using r = 4.78 and h = 2
  4.782  2
143.5607 …
144 (nearest whole)
Number of hours = 90 000  7500
= 12
Firstly, 20 mm = 0.02 m,
Volume = Ah
= 400  0.02
=8
As 1 m3 = 1000 L, then 8m3 = 8000 L.
 volume is 144 m3
 12 hours
 volume of water is 8 m3
 8000 litres is collected.
* These solutions have been provided by projectmaths and are not supplied or endorsed by the Board of Studies
Board of Studies: Notes from the Marking Centre
HSC examination papers © Board of Studies NSW for and on behalf of the Crown in right of State of New South Wales
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1
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HSC Worked Solutions
projectmaths.com.au
Source: http://www.boardofstudies.nsw.edu.au/hsc_exams/
HSC examination papers © Board of Studies NSW for and on behalf of the Crown in right of State of New South Wales