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SPM Mathematics 2019, Paper 2 (Question 11)


Question 11:
Diagram 6 shows a semicircle landscape garden built by Kamal at his house. The garden consists of a herbal garden and a quadrant fish pound. He plans to fence the herbal garden.

Diagram 6

POKQ is a straight line and K is the midpoint of OQ. It is given that PQ = 14 m and OP : OK = 2:1. Calculate
(a) the total length, in m, of the fence for the herbal garden, [3 marks]
(b) the area, in m2, of the herbal garden. [3 marks]


Solution:
(a)
Length of arc PQ=180o360o×2πr                           =180o360o×2×227×7                           =22 mLength of arc LK=90o360o×2×227×3.5                           =5.5 mTotal length of fence=(22+3.5+5.5+3.5+7)m                                =41.5 m

(b)
Total area of semicircle=12πr2                                     =12×227×72                                     =77 m2Total area of quadrant of fish pond=14πr2=14×227×3.52=9.625 m2Area of herbal garden=77 m29.625 m2                                  =67.375 m2



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