WMA11 June 2022

• WMA11/01 Edexcel IAL P1 June 2022, Q8​​ (Radian)

Figure 3 shows a sketch of the outline of the face of a ceiling fan viewed from below.​​ 

The fan consists of three identical sections congruent to OABCDO, shown in Figure 3, where​​ 

• OABO is a sector of a circle with centre O and radius 9 cm​​ 

• OBCDO is a sector of a circle with centre O and radius 84cm​​ 

• angle​​ AOD =2π3​​ radians​​ 

Given that the length of the arc AB is 15 cm,​​ 

• show that the length of the arc CD is 35.9cm to one decimal place.​​ 

(3)

The face of the fan is modelled to be a flat​​ surface.​​ 

Find, according to the model,​​ 

• the perimeter of the face of the fan, giving your answer to the nearest cm,​​ 

(2)​​ 

• the surface area of the face of the fan.​​ 

Give your answer to 3 significant figures and make your units clear.​​  

(5)

SOLUTION​​ 

a- Considering sector AOB

l=rθ

15=9AOB

<AOB=159

<AOB=53 

So the angle COD is​​ 

<COD=2π3-53

<COD=2π-53

So the arc length CD can be found using the arc length formula once again.​​ 

lCD=rθ

=84 x2π-53

=35.929

lCD=35.9 cm  

b-​​ 

P=3lCD+2lAB+6(BC)

P=3(35.929…)+3(15)+6(84-9)

P=3(35.929…)+3(15)+6(75)

P=602.787

P=603 cm

c-​​ 

A=12r2θ

SA=3 x12 x 92 x53+3 x12 x 842 x2π-53

SA=4729.577 .. . ..

SA=4.73 cm2