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)
$\begin{array}{l}\text{Length of arc }BE\\ =\frac{50}{360}\times 2\times 3.142\times 8\\ =6.9822\\ =6.98\text{ m}\end{array}$

(ii)
$\begin{array}{l}\text{Length of arc }CD=9.95\text{ m}\\ \frac{50}{360}\times 2\times 3.142\times r=9.95\\ r=\frac{9.95\times 360}{50\times 2\times 3.142}\\ r=11.40\text{ m}\\ \\ \text{Distance between }CD\text{ and }BE\\ =11.40-8\\ =3.40\text{ m}\end{array}$

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)
$\begin{array}{l}\text{Length of floor of room }Q\\ =\frac{800\text{ cm}}{200}\\ =4\text{ cm}\end{array}$

(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