1. 1
F F F
1. F
2. F F F 1 F
3. ก F F F
4. ก F F ก F Fก F
5. F ก F F ก F F

2. 2
: F F
F OI F ก AI , BI CI ∆OAI ∆OBI
∧ ∧
1. OIA OIB F
2. ∆OAI ∆OBI
3. OA2 = OI2 + AI2 F
4. OB2 = OI2 + BI2 F
5. OA2 = OB2 F
6. OI2 + AI2 = OI 2+ BI2
7. AI2 = BI2
8. AI = BI F
9. BI = CI F

3. 3
: ก FF
1. F 14
24
ก ∆OXY ก
F OY2 = OX2 + XY2
=
=
OY = 25
ก F F F Fก
1
F = 4 × ( × 14 × 25 )
2
=
=
= 196
=
=

4. 4
: ก F F
1. F F 30
25
ก ก F FF
1
OF = AB
2
=
=
EF =
=
EO =
=
ก ก EOF FF
EF2 =
. . =
EO2 =
=
EO = 20
1
ก = × ×
3
=
=
= 6,000 ก กF

5. 5
: ก F F
1. F F 8 F กF 6
13
ก ก F FF AB = 8
AD = 6
BE = 13
DO =
=
(2) ก ก EOB F BO ก EO F
ก (1) BO =
ก ก ABD FF
2
BD =
=
=
BD = 10
BD =
=
= 5
ก ก EOB FF
BE2 =
=

6. EO2 =
=
EO = 12
1
= × ×
3
=
=
= ก กF

7. 6
: F ก ก ก F F
1. F F ก ก ก ก ก กก
F F F
ก F
1. F
2. F F ก ก ก
3. F F ก ก
( Fก F ก ก F ก )
1. F = 2 × ( π(152) - π(52) )
= 2× ( )
= 2 × 200π
= 400π
2. F F ก ก ก = 2 π(15)(30)
=
3. F F ก ก = 2π(5)(30)
=
F F = 400π + +
= 1,600π
≈ 1,600 ×
F F F = 5,024
2. ก ก 15 21

8. ก ก = 2πr2
=
= 450π
F ก ก =
=
= 630π
ก ก=
=
ก ก =
=

9. 7
: ก ก ก FF
1. ก ก r h
F
(1.1) r = 6 h = 10
ก ก = πr 2h
=
=
≈
= 1,130.4 ก กF
(1.2) r = 10 h = 2
ก ก =
=
=
≈ 200 × 3.14
= ก กF
(1.3) r = 3.5 h = 3
ก ก =
=
= 36.75π
≈
= ก กF

10. 8
1. F ก ก 1,727 ก กF F กF
F
5 F F กF F F ก FF
F r = กF F
h = F
F = πr 2h
1,727 = 3.14 × 52 × h
h =
= 22
F F 22
F F =
=
= 690.8
กF F =
= 78.5

11. 9
: ก ก F ก ก ก F
ก กF
1. ก F
2. ก F
3. ก F
4. ก F
5. ก F

12. 10
: ก ก F F
1. ก F h F l F F
h = 12 , l= 15
F = r
2
15 = r2 + 122
225 =
r2 =
=
r =
ก = πr 2h
=
=
F ก =
=
=
ก =
= 216π

13. 11
1. ก ก ก F ก 15 F Fก
20 ก F กF ก ก F
F l =
ก
l 2 = 202 × 502
=
=
l = 25
ก ก =
= 450π + 600π
=
ก =
=
=
ก F กF ก ก F =
= 450π
12

14. : ก ก F F
1. ก F 24 26 F
ก
F ก r F
r2 =
=
=
r =
ก ก ก =
ก = 800π ก กF F
F ก 2 ,512 ก กF F
13

15. : F F ก F
1. F ก ก 60 F F Fก
50 F F F F ก F F
ก F F Fก ก 24 20
ก F F F F ก Fก
F F ก
ก
ก ก
ก ก =
= ก กF
ก
F h = ก
202 =
400 =
h2 = = =
h = 16
ก
ก =
= 768π ก กF
ก
ก ก =
ก
≈ 48.8 = 49
F F F F 49 ก
14
: F F ก F

16. 1. ก F F Fก 30 π ≈ 3.14
F r = ก
r = ก F
ก =
=
=
2. ก F F Fก 15 π ≈ 3.14
F r = ก
r =
ก = πr2
=
=
3. ก 10 π ≈ 3.14
ก = 4πr2
=
=
4. ก 5 π ≈ 3.14
ก =
=
=
15

17. : F F ก F
1. ก F F ก กF ก
( F ) F F
F F ก F
1. ก ( 15 )
2. F ก ก
3. ก
ก =
=
=
F ก ก=
=
=
ก =
=
=
F F =
= 1,275π
1,275
16

18. : ก Fก r F F
1. r = 6
4
ก = πr3
3
=
= 288π ก กF
2. r = 1.5
ก =
=
= 4.5π ก กF
3. r = 10
ก =
=
= 1,333.3π ก กF
4. r = 5
ก =
=
= ก กF
1.17

19. : F F ก F
1. ก Fก ( F F )ก Fก
ก F ก Fก F F Fก ก F
F r =
ก =
ก =
ก Fก
4
4πr2 = πr3
3
1 =
r = F
ก = 3 F
F ก =
= 6 F
ก =
= ก กF F
ก กF F
18
: F F ก F

20. 1. ก F ก 324π F
ก
F ก r F
ก = 4π r2
324π =
r2 =
= 81
r =
ก =
=
= 972π ก กF F
972π ก กF F
2. ก F ก 2,304π ก กF F ก
F r = ก
2,304π =
r3 =
r =
ก =
=
= 576π F
576π F