8. The area of the unshaded region is 2 cm2 .
Triangle BOC has a right angle at O.
The radius of the circle is closest to
A 0.9 cm
B 1.6 cm
C 2.2 cm
D 2.6 cm
E 3.6 cm
9. The solid OPQR, as shown opposite, is one-eighth of a sphere of radius 15 cm.
The point O is the centre of the sphere and the points P, Q and R are on the surface of the
sphere.
∠POQ = ∠QOR = ∠ROP = 90°
The total surface area of the solid OPQR, in cm2, is closest to:
A 619
B 648
C 706
D 884
E 1767
Further Mathematics Unit 4 Page 4 Week 5 SEND Work
10. Melbourne and Hokkaido Island in Japan lie on the same line of longitude and are 9094 km
apart. If Melbourne has a latitude of 37. 83° S, find the latitude of Hokkaido Island, which is
north of Melbourne. Give your answer correct to 2 decimal places.
Answer: _________° N
The following information relates to questions 11 and 12.
A cargo ship travels from Perth (115°E longitude and latitude 33°S) to Cape Town,
South Africa (20° E longitude and latitude 33°S). The ship set sail at 4.00 am on 3 April and
travelled at an average speed of 15 m/s.
11. If the journey from Perth to Cape Town was 8700 km, calculate the duration of the trip correct
to the nearest minute.
Answer: __________ minutes
12a Find the date and time in Perth when the ship arrived at Cape Town.
b Find the time difference in hours between Perth and Cape Town.
c Find the date and local time of the ship’s arrival in Cape Town.
Answers:
12a. ______ April ______ ______(a.m. / p.m.)
12b. The time difference between Perth and Cape Town is ______ hours
12c. ______ April ______ ______(a.m. / p.m.)
604
FM SAC 1- Unit 4
2032 VISION FOR THE OLYMPICS
Question I
For the 2032 Olympic games in Brisbane, the swimming pool will be built as shown in the
diagram below. The surface of the water forms a rectangle 50 metres in length and 25 metre s
wide. At one end of the pool the depth is 2 metres and at the other end its depth is 3.2 metres .
!) O~ I
a. Wh at is th e area of th e wa ter surface (top) of the fu ll- size vers io n of the swimming
po ol?
b. Find the area of the inclined bottom of the pool. Round it to three decimal places .
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FM SAC 1- Unit 4
c. Find the to tal s ur face area of a ll internal surfaces of the full-size version the above
Olympic poo l. Round it to thr ee decimal places.
d. Calculate the volume of water required to fill the Olympic pool. Round it to three
decimal places.
e. If a wa terproo fing pain t is used to a thickness of2mm, how many litres of paint will
be req uired to app ly one coa t for the internal surfaces of the swimming pool? Ignore
any poss ible o ve rl aps where s urfaces meet.
f. If th e wa terproofi ng pai nt costs $140 pe r litre how much will it cost to paint the
int e rnal sur faces of th e sw imm ing poo l?
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FM SAC 1 – Unit 4
g. A_ model is made of the pool with dimensions that are 1/SO’b of the actual dimensions.
Find the internal surface area of this model.
Question 2
The Anna Mears Velodrome will be used for the cycling events. The radius of the in s ide of
the track at each ends of the sprinters line is 30m and the straight section of the track is 170m .
How many times will competitors need to go around the track if they are competing in a
pursuit race (inside track)? Round to the nearest number of lap s.
Choose one of: 2000m, 4000m, 5000m, 10000m, 20000m distance, circ le yo ur se le ction.
Note: Cyclist race along the sprinter‘s line. Justify your answer.
\
“F inish lne
rsut11ne
·—-.__
Sl,)’er’s
Int
Sllfilters
line
200m lloe
M…..- lng
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FM SAC 1- Un it 4
Question 3
Two netba ll ers have started practising netba ll hoping to be good enough to make the
netba ll team in 2032. ‘
Th e ang le of elevation fro m the red ball to the top of the goa lpost is 40°. The angle of Lee ‘ s hand
to the goa l post is 60°.
a. Find a ll four unknown internal angles and label th ose in the given diagram .
Lee Al ia
b. Find the direct distance between Lee’s hand and th e to p ofthi, goalpost.
c. Ca lcul ate the horizona l di stance be t~ een the ball and the goalpost. Justify your
an swe r and round it to th e nearest centi metre.
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~ c1-un;14
Question 4
Lots of young trees will b I dt . 11 e P ante to e nh ance th e garden areas around the venues. The
rees w1 need to be planted h rtl h . .f h s o Y so t at they can grow to their desired height by the
ime I e Olympics are ready to be held.
The young saplings wil l be planted and protected by square based pyramid shaped
guards.
..
‘
: 54cm
:
–•
When the trees have grown sufficien tl y, I/3 rd of the top section of the tree guard is
removed along the dotted line to a ll ow the tree to grow further. Removing this top
section, decreases the height of the tree guard to “x” cm , as shown in the diagram below.
Discuss what is the ratio of the volume of the t re e guard that is removed to the volume
of the tree guard that remains, justifyi ng your answe r.
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FM SAC 1 – Unit 4
Question 5
The Olympic d~l ega_t~s that have come to inspect the venues decide that the want to visit
so me other cap ital cities of Australia while they are here. They could go to Adelaide directly
or go to Ade laide via Melbourne.
Br is bane is 9 18 km north of Melbourne and Melbourne is 131 O km east of Adelaide.
a. Draw a labelled diagram
b. Ca lc ulate the bearing of Adelaide from Brisbane.
Question 6
The Olymp ic Games will be viewed from many different locations around the world.
Cooktown at I 5° S and 145° E and in Melbourne at 37° S and 145 ° E are located on the same
meridians of longitude.
Di scuss what is the shortest d istance is on the merid ian running between these two
locat io ns.
(Radius of the earth 6400km).
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FM SAC 1- Unit 4
Question 7
There are some delegat fl · • . . .. es ymg m to see the progress of the construction and while m
Brisbane they are going to visit some of the attrac ti ons nearby.
T~ey are go in g to Moreton Island to visit Tangalooma by Ferry on th e first stage of the
tnp . Moreton Island is on a bearing of75o from Brisbane and is 46.7km from Bris bane.
From Moreton Island they will travel to Rainbow beach on a bearing of324° and the
distance is between 143 km .
Rainbow Beach
Moreton Island
Brisb an e
a. Calcula te the bearing of Moreton island fro m Rainbow Beach. Justify your
answer and in clude measurement of angles in the abo ve diagram.
b. Ca lculate th e direct distan ce of Brisbane from Rainbow Beach. Justify your
answer and include a diagram.
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FM SAC 1 – Unit 4
a) Find the distance from London to the Sea of Okhostk.
b) Find the d is tance fr om the Sea ofOkho stk to Me lb ourne
c) The di stance from London to Melbourne in a direct line is 16 973 km. Us ing your
answers to Question 8 a an d Question 8 b, determi ne whether Pythagora
