year 8 maths

Chapter review
193
Extended-response questions
1 A company makes square nuts for bolts to use in building construction and steel structures. Each nut
starts out as a solid steel square prism. A cylinder of diameter 2 cm is bored through its centre to make
a hole. The nut and its top view are shown here.
2 cm
2 cm
4 cm
4 cm
4 cm
4 cm
The company is interested in how much paint is required to paint the nuts. The inside surface of the
hole is not to be painted. Round all answers to two decimal places where necessary.
a Find the area of the top face of the nut.
b Find the total outside surface area of the nut.
c If the company makes 10000 nuts, how many square metres of surface needs to be painted?
The company is also interested in the volume of steel used to make the nuts.
d Find the volume of steel removed from each nut to make the hole.
e Find the volume of steel in each nut.
f Assuming that the steel removed to make the hole can be melted and reused, how many nuts can
be made from 1 L of steel?
2 A simple triangular shelter has a base width of 2 cm , a height of 2 m and a length of 3 m .
2 m
3 m
2 m
a Use Pythagoras’s theorem to find the hypotenuse length of one of the ends of the tent. Round the
answer to one decimal place.
b Assuming that all the faces of the shelter including the floor are covered with canvas material, what
area of canvas is needed to make the shelter? Round the answer to the nearest whole number of
square metres.
c Every edge of the shelter is to be sealed with a special tape. What length of tape is required?
Round to the nearest whole number of metres.
d The shelter tag says that it occupies 10000 L of space. Show working to decide if this is true or
false. What is the difference?
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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