Cambridge Additional Mathematics

The unit circle and radian measure (Chapter 8) 207

8 The cone is made from this sector:

Find, correct to 3 significant figures:

a the slant lengthscm b the value ofr

c the arc length of the sector d the sector angleμin radians.

9 The end wall of a building has the shape illustrated, where

the centre of arc AB is C. Find:

a ®to 4 significant figures

b μto 4 significant figures

c the area of the wall.

10 [AT] is a tangent to the given circle. OA=13cm and

the circle has radius 5 cm. Find the perimeter of the shaded

region.

11 Anautical mile(nmi) is the distance on the Earth’s surface

that subtends an angle of 1 minute (or 601 of a degree) of the

Great Circle arc measured from the centre of the Earth.

Aknotis a speed of 1 nautical mile per hour.

a Given that the radius of the Earth is 6370 km, show that

1 nmi¼ 1 : 853 km.

b Calculate how long it would take a plane to fly from

London to Moscow (a distance of 2508 km) if the plane

can fly at 480 knots.

12 A sheep is tethered to a post which is 6 m from

a long fence. The length of rope is 9 m. Find

the area which the sheep can feed on.

rcm

μ

10 cm

12 cm

scm

fence

post sheep

6 m

30 m

5 m

A B

C

μ°®°

O

T

A

N

S

C

P

1 ' Q

1 nautical mile

()nmi

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_08\207CamAdd_08.cdr Monday, 6 January 2014 11:41:22 AM BRIAN