Chapter 1 Circular Measure (1.4)

In the diagram, O is the centre of a circle with radius 6 cm. TR and TS are tangents to the circle at R and S respectively, with  $\angle ORT=\angle OST=\frac{\pi}{2}$ radians. Given TR = 14 cm and   $\angle RTS=\theta$ radians. Find the value of  $\theta$  and the perimeter, in cm, of the shaded region.

• 0.405, 30.430 

• 0.810, 42.430 

• 0.810, 41.992 

• 2.332, 53.992 

A cone has a base radius of 3 cm and a height of 4 cm. This cone is opened up to form a sector POQ as shown in the diagram. Given $\angle POQ=\theta$ radians, find the value of  $\theta$ and the area of the sector POQ, in  $cm^2$ .   

• 3.77, 30.160        

• 3.77, 47.125

• 4.19, 30.160

• 4.19, 47.125

The diagram shows the cross-section of a round cake with centre O and radius 7 cm. The top part of the cake is cut along AB and is filled up with cake toppings. Given that AB = 12 cm, find the area of the cross-section of the cake, in cm², which has been removed.

• 21.63

• 28.84

• 32.91

• 50.47

The diagram shows the cross-section of a meat ball. The meat ball is spherical-shaped with a radius of 5 cm and the lower portion is cut off along AB. Given that AB = 8 cm. Find the perimeter, in cm, of the cross-section of the meat ball.

• 12.346

• 18.751

• 22.145

• 30.145

The wall at the end of the ward is in the form of a sector PQR with centre R as shown in the diagram. Find the area of the wall, in cm².

• 320.14

• 345.68

• 363.53

• 387.244

A goat is tied by a rope to a pole which is 6 m from the fence. Given that the length of the rope is 9 m. Find the feeding area, in m², of the goat.

• 226.63

• 245.12

• 258.34

• 260.02

The diagram shows a solid disc with radius 40 cm and some parts are painted brown. The empty smaller circle with the same centre has a radius of 10 cm. Find the area of the solid disc that is not painted brown, in cm².

• 1 125

• 3 588

• 4 713

• 5 027

The photo shows a clock. The minute hand is 10 cm long. What is the length travelled by the tip of the minute hand in 20 minutes?

• 10.47

• 15.71

• 20.95

• 26.18

The diagram shows 8 lane running track in a stadium which is made up of a rectangle of length 84.39 m and semicircle at each end. The radius of the first and second semicircle is 36.8 m and 38.02 m respectively. How far does a runner run if he runs in the first lane and makes a complete circuit, in m?

• 400

• 402

• 407

• 408

The diagram shows 8 lane running track in a stadium which is made up of a rectangle of length 84.39 m and semicircle at each end. The radius of the first and second semicircle is 36.8 m and 38.02 m respectively. During a warm-up session, Mukhriz and Habil complete one circuit in the second and third lane of the running track. Find the difference in distance, in m, between the two runners.

• 7.25

• 7.50

• 7.66

• 7.80