year 8 maths

188 Chapter 3 Measurement and Pythagoras’ theorem
1 A cube has capacity 1 L . What are its dimensions in cm, correct to one decimal place?
2 A fish tank is 60 cm long, 30 cm wide, 40 cm high and contains 70 L of water. Rocks with a volume of
3000 cm 3 are placed into the tank. Will the tank overflow?
Puzzles and challenges
3 What proportion (fraction or percentage) of the semicircle does
the full circle occupy?
4 What is the distance AB in this cube?
(Pythagoras’ theorem is required.)
5 By what number do you multiply the radius of a circle to double its area?
6 Find the exact value (as a surd) of a in this diagram.
(Pythagoras’ theorem is required.)
1
1
A
a
1
1 m
B
1
1 1
1
7 A cube of side length 3 cm has its core removed in all directions, as shown. Find:
a its inner surface area
b its outer surface area
3 cm 1 cm
1 cm
3 cm
8 A square just fits inside a circle. What percentage of the circle is occupied by the square?
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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