Page 124 - Mathematics_Form_3

Circles

πr
Example 5.1 l = ____
θ .
180°
An arc of a circle with radius 3 cm Substituting the given values into the
subtends a central angle whose measure formula gives,
is 60°. Calculate the length of the arc 22 × 1080 cm × 105°
_________________
FOR ONLINE READING ONLY
(leave your answer in terms of ). l = 7 × 180°
Solution = 1980 cm
Given r = 3 cm and θ = 60° . The arc
length of a circle is given by, Therefore, the arc length of the
garden plot is 1980 cm.
πr
θ .
l = ____
180° (b) Perimeter = OA + OB + AB
Substituting the given values, it follows
= 1080 cm +1080 cm +1980cm
that
3 cm × π = 4140 cm
_____
l = × 60°
180° Therefore, the perimeter of the
= cm garden is 4140 cm.
Therefore, the length of the arc is cm.

Example 5.2 Exercise 5.2

The following figure represents the 1. A circular loaf of bread has a mass
shape of a garden plot. of 2 kg. If 0.75 kg of the bread is
O to be given to a friend, explain how
are you going to divide the bread
1080 cm 105º
without using a weighing balance.
A B 2. What is the size of the central angle
for a circle of radius 9 cm and an
arc length of 3 cm?
If its central angle is 105° and the radius 3. Find the length of an arc of a circle
is 1080 cm, calculate: Mathematics for Secondary Schools
of radius 1cm with a central angle
(a) The arc length of the garden plot. of 90° (Use π = 3.14).
22
___
Use π = .
7 4. A roundabout at a certain road
(b) The perimeter of the garden. junction has a radius of 15 m. A
car drives around the roundabout,
Solution
turning through an angle of 140°.
(a) Given r = 1 080 cm and θ = 105° .
The arc length, l is given by, What distance does the car travel?

Student\s Book Form Three 117

18/09/2025 09:59:35
MATHEMATIC F3 SB.indd 117 18/09/2025 09:59:35
MATHEMATIC F3 SB.indd 117