Page 67 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure

Example of HOTS 14
HOTS Question
French drain using perforated circular pipes is a The diagram below shows sector MON of a circle. The
very effective rainwater management in solving length of chord MN = 11 cm.
landscaping water issues. The diagram below shows
the cross section of the circular pipe used in the
French drain. The pipe is partially filled with water N 14 cm
that accumulates as rainwater flows into it. 11 cm
O
1
Minion Pro 10pt = — M
2
----------------------------------------
Arial 8.5pt = 1 O 5 cm Find the area, in cm , of the shaded segment.
2
2 2 rad
1
Arial 8pt =
2 Solution
---------------------------------------- If the length of the circular pipe is 20 cm, calculate For ΔMNO,
the volume, in cm , of the water collected.
3
2
2
2
Cth KBAT_Optima 9pt = 80 11 = 14 + 14 – 2(14)(14)(cos ∠MON)
1.25
---------------------------------------- Solution 14 + 14 – 11 2
2
2
Cross sectional area of the accumulated water cos ∠MON =
---------------------------------------- = r (q – sin q) 2(14)(14)
1 2
2 = 0.6913
1
= (5) (2 – sin 2)
2
–1
2 ∠MON = cos (0.6913)
2
= 13.63 cm
1 = 0.8075 rad
Volume of the accumulated water
1
XX Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
A
= r q
2
= Cross sectional area × Length of circular pipe sector 2
Penyelesaian = 13.63 × 20
1
(a) XX = 272.6 cm 3 = × 14 × 0.8075
2
2
= 79.135 cm
2
Try this HOTS Question
1
The circular pipes are widely used in sewage s = (2r + p)
2
treatment system. The diagram below shows the
sewage collected in the circular pipe. 1
= [2(14) + 11]
2
= 19.5 cm
O 4 m
1.8 rad A triangle = s(s – p)(s – r) 2
Sewage
Form 5
= 19.5(19.5 – 11)(19.5 – 14)
2
Calculate the volume, in m , of the sewage = 70.81 cm
2
3
collected in the circular pipe with the length of
1.5 km. Area of shaded segment = A sector – A triangle
Answer: 9 913.5 m 3 = 79.135 – 70.81
= 8.325 cm 2
Try Question 8 in ‘Try This! 1.3’
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