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= 180 o 360 o ×2πr                            = 180 o 360 o ×2× 22 7 ×7                            =22 m Length of arc LK= 90 o 360 o ×2× 22 7 ×3.5                            =5.5 m Total length of fence=( 22+3.5+5.5+3.5+7 )m                                 =41.5 m

(b)
Total area of semicircle= 1 2 π r 2                                      = 1 2 × 22 7 × 7 2                                      =77  m 2 Total area of quadrant of fish pond = 1 4 π r 2 = 1 4 × 22 7 × 3.5 2 =9.625  m 2 Area of herbal garden=77  m 2 9.625  m 2                                   =67.375  m 2



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