 # Circular Measure Short Questions (Question 1, 2 & 3)

Question 1:

The figure shows the sector OCB of radius 13 cm at the centre O. The length of the arc CB = 5.2 cm. Find
(a) the angle in radians,
(b) the perimeter of the shaded region.

Solution:
(a)

(b)

Perimeter of the shaded region = 5.07 + 1.03 + 5.2 = 11.3 cm.

Question 2:
The figure shows the sector AOB of a circle, centre O and radius 5 cm. The length of the arc AB is 6 cm. Find the area of:
(a) the sector AOB,
(b) the shaded region.

Solution:
(a) Arc AB = 6cm
s = θ
6 = 5 θ
θ = 6/5 rad

(b)

Question 3:
Diagram below shows a sector QOR of a circle with centre O.

It is given that PS = 8 cm and QP = PO= OS = SR = 5 cm.
Find
(a) the length, in cm, of the arc QR,
(b) the area, in cm2, of the shaded region.

Solution:
(a) Length of arc QR = θ = 10 (1.75) = 17.5 cm

(b)
Area of the shaded region
= Area of sector QOR – Area of triangle POS
½ (10)2 (1.75) – ½ (5) (5) sin 1.75 (change calculator to Rad mode)
= 87.5 – 12.30
= 75.2 cm2

### 1 thought on “Circular Measure Short Questions (Question 1, 2 & 3)”

1. Nice questions. Good revision.