**Question 4**:

Diagram below shows a circle with centre

*O*.The length of the minor arc is 16 cm and the angle of the major sector

*AOB*is 290^{o}.Using π = 3.142, find

**(a)**the value of θ, in radians. (Give your answer correct to four significant figures)

**(b)**the length, in cm, of the radius of the circle.

*Solution:***(a)**

Angle of the minor sector

*AOB*= 360

^{o }– 290^{o }= 70

^{o }= 70

^{o }× $\frac{3.142}{180}$=

**1.222 radians**

**(b)**

Using

*s*=*rθ**r*× 1.222 = 16

**radius,**

*r*= 13.09 cm**Question 5**:

Diagram below shows sector

*OPQ*with centre*O*and sector*PXY*with centre*P.*Given that

*OQ*= 8 cm,*PY*= 3 cm , ∠*XPY*= 1.2 radians and the length of arc*PQ*= 6cm ,calculate

**( a)**the value of θ , in

*radian ,*

**( b)**the area, in cm

^{2}, of the shaded region .

*Solution:***(a)**

*s*=

*r*θ

6 = 8 θ

θ = 0.75 rad

**(b)**

Area of the shaded region

= Area of sector

$=\frac{1}{2}{\left(8\right)}^{2}\left(0.75\right)-\frac{1}{2}{\left(3\right)}^{2}\left(1.2\right)$
*OPQ*– Area of sector*PXY*= 24 – 5.4

=

**18.6 cm**^{2}**Question 6**:

Diagram below shows a circle with centre

*O*and radius 12 cm.Given that

*A*,*B*and*C*are points such that*OA*=*AB*and ∠*OAC*= 90°, find**(a)**∠

*BOC*, in radians,

**(b)**the area, in cm

^{2}, of the shaded region.

*Solution:***(a)**For triangle

*OAC,*

cos ∠

*A**OC*= 6/12 Ð

*A**OC*= 1.047 rad (change calculator to Rad mode)**Ð**

*B*

*OC*= 1.047 rad**(b)**

Area of the shaded region

= Area of

*BOC*– Area of triangle*AOC*= ½ (12)

^{2}(1.047) – ½ (6) (12) sin 1.047 (change calculator to Rad mode)= 75.38 – 31.17

=

**44.21 cm**^{2}