The helicopter is elevated an additional 15 metres away from the ground. The diameter of the circular area of light on the ground is now closest to: A. 8 m; B. 13 m; C. 15 m; D. 20 m; E. 25 m

Further Mathematics Unit 4 Page 1 Week 2 SEND Work
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Show the essential working in the spaces provided for ALL questions.
A search and rescue helicopter shines a light down from a vertical height of 50 metres as shown below. The circular area of light it creates on the ground has a diameter of 10 metres.

Question 1
The helicopter is elevated an additional 15 metres away from the ground. The diameter of the circular area of light on the ground is now closest to
A. 8 m
B. 13 m
C. 15 m
D. 20 m
E. 25 m

Question 2
The helicopter moves to a height so that the diameter of the circular area increases from 10 metres to 40 metres.
The area of the circular light is now
A. four times what it was before.
B. eight times what it was before.
C. sixteen times what is was before.
D. thirty-two times what is was before.
E. sixty-four times what it was before.

Further Mathematics Unit 4 Page 2 Week 2 SEND Work

Question 3
The value of x in the following figure is 3.
A. 20
B. 25
C. 33
D. 45
E. 55

[Hint: Separate out the similar triangles and match up the corresponding sides and angles]

Question 4
Ben is making a 1:100 model of a car with an engine capacity of 2.3 litres (2300cm3 ). If Ben wants to include a scale model of the engine, then the capacity of the model engine should be
A. 0.0023 cm3
B. 0.023 cm3
C. 0.23 cm3
D. 2.3 cm3
E. 23 cm3

Question 5
Triangle ABC is similar to triangle AXY.
AX = 3
2 AB
If the area of ∆ABC = 108 cm2 , the area of ∆AXY is
A. 32 cm2
B. 48 cm2
C. 54 cm2
D. 72 cm2
E. 81 cm2
B
X
A C
Y
2522
10
x

Further Mathematics Unit 4 Page 3 Week 2 SEND Work

Question 6
A cylindrical block of wood has a diameter of 12 cm and a height of 8 cm.
A hemisphere is removed from the top of the cylinder, 1 cm from the edge, as shown below.
The volume of the block of wood, in cubic centimetres, after the hemisphere has been removed is closest to
A. 452
B. 606
C. 643
D. 1167
E. 1357

Question 7
A triangular prism with a cross-section of an equilateral triangle is shown on the right.
The side lengths of the triangle are 4cm and the length of the prism is 10cm.
The total surface area in square cm is
A. 46.93
B. 80
C. 93.86
D. 126.93
E. 133.86
4 cm
10 cm