13. Find x in terms of z
z
h
x (x,z)
1 1 x
b b
2 2
14. Find x in terms of z
z
h
x (x,z)
1 1 x
b b
2 2
Method 1 : using similar s
15. Find x in terms of z
z
h
x (x,z)
1 1 x
b b
2 2
Method 1 : using similar s
h
1
b
2
16. Find x in terms of z
z
h
x (x,z)
1 1 x
b b
2 2
Method 1 : using similar s
h
1
b
2
h-z
x
17. Find x in terms of z
z
h
x (x,z)
1 1 x
b b
2 2
Method 1 : using similar s
h hz
h
1 x
b
1 2
b
2
h-z
x
18. Find x in terms of z
z
h
x (x,z)
1 1 x
b b
2 2
Method 1 : using similar s
h hz
h
1 x
b
1 2
b 2h h z
2
b x
h-z b h z
x
x 2h
19. Find x in terms of z Method 2 : using coordinate geometry
z
h
x (x,z)
1 1 x
b b
2 2
Method 1 : using similar s
h hz
h
1 x
b
1 2
b 2h h z
2
b x
h-z b h z
x
x 2h
20. Find x in terms of z Method 2 : using coordinate geometry
z
h (0,h)
x (x,z)
1 1 x
b b
2 2
Method 1 : using similar s
h hz
h
1 x
b
1 2
b 2h h z
2
b x
h-z b h z
x
x 2h
21. Find x in terms of z Method 2 : using coordinate geometry
z
h (0,h)
x (x,z)
1 b,0
1 1 x 2
b b
2 2
Method 1 : using similar s
h hz
h
1 x
b
1 2
b 2h h z
2
b x
h-z b h z
x
x 2h
22. Find x in terms of z Method 2 : using coordinate geometry
z
h0
m
h (0,h) 1
0 b
x (x,z) 2
2h
1 b,0 b
1 1 x 2
b b
2 2
Method 1 : using similar s
h hz
h
1 x
b
1 2
b 2h h z
2
b x
h-z b h z
x
x 2h
23. Find x in terms of z Method 2 : using coordinate geometry
z
h0
m
h (0,h) 1
0 b
x (x,z) 2
2h
1 b,0 b
1 1 x 2 2h
b b zh x 0
2 2 b
Method 1 : using similar s
h hz
h
1 x
b
1 2
b 2h h z
2
b x
h-z b h z
x
x 2h
24. Find x in terms of z Method 2 : using coordinate geometry
z
h0
m
h (0,h) 1
0 b
x (x,z) 2
2h
1 b,0 b
1 1 x 2 2h
b b zh x 0
2 2 b
Method 1 : using similar s b z h 2hx
h hz
b h z
h
1 x
b x 2h
1 2
b 2h h z
2
b x
h-z b h z
x
x 2h
25. Find x in terms of z Method 2 : using coordinate geometry
z
h0
m
h (0,h) 1
0 b
x (x,z) 2
2h
1 b,0 b
1 1 x 2 2h
b b zh x 0
2 2 b
Method 1 : using similar s b z h 2hx
h hz
b h z
h
1 x
b x 2h
1 2
b 2h h z Similarly;
2
b x a h z
h-z b h z y
x 2h
x 2h
26. bh z ah z
A z 4
2h 2h
27. bh z ah z
A z 4
2h 2h
abh z
2
h2
28. bh z ah z
A z 4
2h 2h
abh z
2
h2
abh z
2
V 2
z
h
29. b h z a h z
A z 4
2h 2h abh z
h 2
V lim 2
z
z 0 h
abh z
2 z 0
h2
abh z
2
V 2
z
h
30. bh z ah z
A z 4
2h 2h abh z
h 2
V lim 2
z
z 0 h
abh z
2 z 0
ab
h
h2 2 h z dz
2
abh z h 0
2
V 2
z
h
31. bh z ah z
A z 4
2h 2h abh z
h 2
V lim 2
z
z 0 h
abh z
2 z 0
ab
h
h2 2 h z dz
2
abh z h 0
2
V z
ab h z
3 h
2
h 2
h 3 0
32. b h z a h z
A z 4
2h 2h abh z
h 2
V lim 2
z
z 0 h
abh z
2 z 0
ab
h
h2 2 h z dz
2
abh z h 0
2
V z
ab h z
3 h
2
h 2
h 3 0
ab h 3
2 0
h 3
abh
units 3
3
33. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
34. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
35. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
36. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
37. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
38. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
39. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
40. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
41. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
42. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
43. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
44. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
45. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
46. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
x
47. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
2y
x
2y
48. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
A x 4 y 2
2y
x
2y
49. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
A x 4 y 2
44 x 2
2y
x
2y
50. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
y
2
-2 2 x
-2
A x 4 y 2
44 x 2
2y
V 44 x 2 x
x
2y
51. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
44 x 2 x
2
y V lim
x 0
x 2
2
-2 2 x
-2
A x 4 y 2
44 x 2
2y
V 44 x 2 x
x
2y
52. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
44 x 2 x
2
y V lim
x 0
x 2
2
2 8 4 x 2 dx
0
-2 2 x
-2
A x 4 y 2
44 x 2
2y
V 44 x 2 x
x
2y
53. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
44 x 2 x
2
y V lim
x 0
x 2
2
2 8 4 x 2 dx
0
2
4 x 1 x 3
8
-2 2 x 3 0
-2
A x 4 y 2
44 x 2
2y
V 44 x 2 x
x
2y
54. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
44 x 2 x
2
y V lim
x 0
x 2
2
2 8 4 x 2 dx
0
2
4 x 1 x 3
8
-2 2 x 3 0
-2 8 8 0
8
3
128
A x 4 y 2 units 3
3
44 x 2
2y
V 44 x 2 x
x
2y
55. (ii) A solid has a circular base, x 2 y 2 4 , and each cross section is
a square perpendicular to the base.
44 x 2 x
2
y V lim
x 0
x 2
2
2 8 4 x 2 dx
0
2
4 x 1 x 3
8
-2 2 x 3 0
-2 8 8 0
8
3
128
A x 4 y 2 units 3
3
44 x 2
2y
V 44 x x
2
Exercise 3A; 16ade, 19
x Exercise 3C; 2, 7, 8
2y