Pythagoras
Pythagoras
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1
A train tunnel is in the shape of part of a circle.
The radius of the circle is 9m.
The width at ground level is 14m
Calculate the height of the tunnel
4Marks
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14.66m
2
A sewage waste pipe cross section is shown.
The diameter of the pipe is 16m.
The surface width AB of sewage is 12m.
Calculate the depth d of the sewage.
4Marks
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13.29m
3
A security lock is being installed on a gate.
The security lock can only function if the corner of the gate it is installed on is 90°
Can this lock function correctly?
4Marks
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The lock will function correctly
4
A doorway is in the shape of part of a circle
The diameter of the circle is 90cm
The width of the door at the ground is 120cm
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157.08cm
5
A football pitch should be in the shape of a rectangle.
The pitch at Tyneside is 60 yards by 91yards.
The diagonal of the pitch is 109 yards.
Is the pitch at Tyneside a rectangle?
Justify your answer.
4 Marks
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Yes.
2 sets of equal opposite sides and right angled corners
6
A cinema banner is made using part of a circle.
The height of the banner is 8·6m.
The radius is 5m.
Determine the width, AB of the banner.
4 Marks
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6.94m
7
A train tunnel cross section is in the shape of part of a circle
The radius of the circle is 11m.
The width of the tunnel at ground level is 18m,
Determine the height of the tunnel.
4 Marks
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17.32m
8
A designer rug is in the shape of part of a circle
The height of the rug is 54cm.
The radius of the circle is 36cm
Determine the width of the rug.
4 Marks
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65.4cm
9
The circular cross section of an oil pipe is shown.
The radius of the pipe is 1.8m
The width AB of the surface level of oil is 2·4m
Determine depth of oil.
4 Marks
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0.46m
10
An advertising banner is designed using 2 identical circles intersecting.
The radius of the circles is 3·6m
The line PQ where the circles join is 4·8m
Calculate the width of the banner.
4 Marks
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2.7m
11
The cross section of a water pipe is shown
The radius of the pipe is 0·9m
The depth of water currently in the pipe is 1·5m at its deepest.
Calculate the width ST at the water level
4 Marks
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1.34m
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