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1 1

2

3 v e f v e + f = 2 (() ( ) + ( ) = 2)

4 ( ) = (1 ) ( ) 2 1 1

5 3 () = (1 ) ( ) (1 )

6 (1) (2)

7 5 (1) (2)

8 (1) (2)

9 7 (1) (2)

10 ( ) ( ) , 2, 3, 4

11 ( i ) 1 ( ii ) (iii) (i), (ii) 2 (ii) 2 (iii) D (1) (2) (3) D F E D,,, E, F, DE, EF, FD 8 (1) 8 D, E, F, EF 4 E, F 2 DE, DF D 2 (2) 8 D 4,, DE, FD 4 D (3) 8 D (1), E, F, EF 4 D (1), EF D

12 ( i ) 1 ( ii ) (iii) P 2 1 Q 2 P 2 Q 2 P, Q PQ P 2 3 (1) (2) (3) (4) D (5) D F E G D H (1) 2 D, FE (2) D,, E, F D E EHD F FG (3) 2

13 11 GHD, EFGH (4) D D 2 4 D E F D G D D DH (5) D D 4 EF, FG, GH, HE

14 P, Q 2 l P l m Q l n m Q n n P Q m n P Q 2 P Q P l m 2 4 D (1) D (2) D E H F G (1) D FE, F F D FE F D FE D 4 FE, FG, GHD, EHD

15 13 (2) D D EFGH

16 (1) (2) (3) (1) (2) (3) (1) (2) 1 (3)

17 (1) (2) (3) l 1 (1) (2) (3) D l l l l (1) l 1 D l (2) l 1 l

18 16 (3) l 1 l

19 (i) 1 (ii) 1 (iii) (1) (2) (3) (1) (2) (3)

20 ( i ) 2 ( ii ) 2 (iii) (i), (ii) 3 4 P G 3 D 3 3 D, P, F P H G E F D, P, F 3 D P DHG D P F FG D F 2 H 2 DHG EF DHG DP EF E F F DP EF D FG EHD FG PF EHD H D PF E F P, Q, R (1) 2 (2) 3 P R P P G P G Q Q R

21 ( i ) ( ii ) (iii) (iv) (ii), (iii) 3 5 (1) (3) (1) D (2) H G (3) E F D D D H G (1) (2) (3) E F D D FG E (1)E F H G (2)H E FG F, G, GF D (3) D

22 20 (1) (3) (1) E (2) H (3) 3 5 P, Q, R D, E, 3 P, Q, R Q P D H R G F G E F D

23 D-EFGH D H X G Y E F XY XY 1 X Y 3 6 (1) (3) (1) (2) (3) X Y X Y X Y

24 22 (1) (2) (3)

25 ( ) = ( ) 2 + ( ) 4 1 (1) (2) 5cm 4cm 4cm (1) (i) 2 4cm (ii) 4cm 4cm 4cm 5cm 5cm ( ) = 4 3 = 12 cm 2 ( ) = ( ) 5 = 14 5 = 70 cm 2

26 24 ( ) = ( ) 2 + ( ) = = 94 cm 2 (2) (i) 2 (ii) 4cm 4cm ( ) = π 3 2 = 9π cm 2 ( ) = ( ) = 2 π 3 = 6π cm ( ) = 4 6π = 24π cm 2 () = ( ) 2 + ( ) = 9π π = 18π + 24π = 42π cm 2

27 ( ) = ( ) + ( ) r cm R cm R cm x ( ) = (2 π R) x 360 cm r cm () = 2 π r cm r cm R cm x r cm R cm ( ) = () (2 π 1 R) x 360 = 2 π 1 r x = 360 r R () = 360 () = 1 2 = 1 2 ( ) ( ) () ( ) = 1 2 2πr R = πrr π ( ) ( ) 4 2 (1) (2) 6cm 9cm 5cm

28 26 (1) (i) (ii) 6cm 5cm 5cm 6cm 5cm 5cm ( ) = 5 5 = 25 cm 2 ( ) = ( ) = 60 cm 2 () = ( ) + ( ) = = 85 cm 2 (2) (i) (ii) 9cm 9cm ( ) = π 3 2 = 9π cm 2 ( ) = π 9 3 = 27π cm 2 () = ( ) + ( ) = 9π + 27π = 36π cm 2

29 () = ( ) () 4 3 (1) (2) 5cm 4cm 4cm (1) () = ( ) () = (4 3) 5 = 12 5 = 60 cm 3 () = () ( ) () () = ( ) () (2) ( ) = ( ) () = (π 3 2 ) 4 = 9π 4 = 36π cm 3

30 () = () 1 3 = ( ) () (1) (2) 4cm 5cm 4cm 5cm 6cm (1) 1 6 cm 4 cm ( ) = ( ) () 1 3 = (6 6 2 ) = 48 cm3 (2) 3 cm 4 cm ( ) = ( ) () 1 3 = (π ) = 12π cm3

31 O r O r 4 S S = πr 2 4 = 4πr 2 O r r 1 1 ( ) = 1 3 ( ) () r () = ( ) V V = ( ) = 1 3 ( ) () = 1 3 ( ) r = 1 3 4πr2 r = 4 3 πr cm () = ( ) () = 4π π 32 = 27π (cm 2 ) ( ) = () 1 2 = ( 4 3 π 33) 1 2 = 18π (cm3 )

2

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