PT3 Mathematics 2017, Question 7


Question 7 (a):
In Diagram 7.1, arcs BE and CD which are centred at A, are the arches of a bridge. The radius used to build arc BE is 8 m.
(i) Calculate the length, in m, of arc BE. Round off the answer to two decimal places.
[Use π = 3.142]
(ii) The length of arc CD is 9.95 m.
Calculate the distance, in m, between arc CD and BE. Round off the answer to two decimal places.
[Use π = 3.142]

Solution:
(i)
Length of arc BE = 50 360 ×2×3.142×8 =6.9822 =6.98 m

(ii)

Length of arc CD=9.95 m 50 360 ×2×3.142×r=9.95 r= 9.95×360 50×2×3.142 r=11.40 m Distance between CD and BE =11.408 =3.40 m

Question 7 (b):
Diagram 7.2 shows the floor plan for rooms P and Q which are rented by Syarikat Mesra.
(i) State the length, in cm, floor room Q which has been redrawn using scale 1 : 200.
(ii) A rectangular mat with the length of 4 m and the perimeter of 13 m is placed on the floor in room P.
Calculate, in m2, the area of the floor space of room P that is not covered by the mat.

Solution:
(i)
Length of floor of room Q = 800 cm 200 =4 cm

(ii)


Area of mat = 4 × 2.5
= 10 m2
Area of room P = 7 m × 5 m
= 35 m2
Area of floor space of room P that is not covered by the mat
= 35 – 10
= 25 m2


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