6.2 Hojiirraa Oolmaa Geengoo
1. Kaayyoo Barumsaa
- Naannawaa (Circumference) geengoo herreeguu ni danda’u.
- Bal’ina (Area) geengoo ni barbaadu.
- Rakkoolee jiruuf jireenyaa geengoon walqabatan hiikuu ni baru.
2. Yaadannoo (Key Notes)
- Pi (π): Gatii isaa tilmaamaan 3.14 ykn 227dha.
- Naannawaa (C): Sarara alaa geengoo. C = 2πr ykn C = πd.
- Bal’ina (A): Hamma lafa geengoon qabate. A = πr2.
- Raadiyasiin (r) daayaameetira (d) harka walakkaa (d2) ta’uu isaa dagatin.
3. Fakkeenyota (Examples)
1. Geengoo raadiyasiin isaa 7cm ta’eef naannawaa isaa barbaadi.
Deebii: C = 2 × (22/7) × 7 = 44 cm.
Deebii: C = 2 × (22/7) × 7 = 44 cm.
2. Geengoo raadiyasiin isaa 10cm ta’eef bal’ina isaa barbaadi. (π = 3.14)
Deebii: A = 3.14 × 102 = 3.14 × 100 = 314 cm2.
Deebii: A = 3.14 × 102 = 3.14 × 100 = 314 cm2.
3. Daayaameetirri geengoo tokkoo 14m yoo ta’e, naannawaa isaa meeqa?
Deebii: C = (22/7) × 14 = 44 meetira.
Deebii: C = (22/7) × 14 = 44 meetira.
4. Naannawaan geengoo tokkoo 62.8 cm yoo ta’e, raadiyasii isaa barbaadi. (π = 3.14)
Deebii: r = C / (2π) = 62.8 / 6.28 = 10 cm.
Deebii: r = C / (2π) = 62.8 / 6.28 = 10 cm.
5. Bal’inni geengoo tokkoo 154 cm2 yoo ta’e, raadiyasii isaa barbaadi.
Deebii: r2 = A / π = 154 / (22/7) = 49. √49 = 7 cm.
Deebii: r2 = A / π = 154 / (22/7) = 49. √49 = 7 cm.
4. Gaaffilee Shaakalaafi Ibsa (15)
1. Foormulaan naannawaa geengoo maali?
Deebii: C = 2πrIbsa: r-n raadiyasii geengooti.
2. Foormulaan bal’ina geengoo maali?
Deebii: A = πr2Ibsa: Raadiyasii iskuweerii goonee Pi-n baay’isna.
3. Yoo r = 7cm ta'e, naannawaan meeqa?
Deebii: 44 cmIbsa: 2 × (22/7) × 7 = 44.
4. Yoo r = 14m ta'e, bal’inni meeqa?
Deebii: 616 m2Ibsa: (22/7) × 14 × 14 = 44 × 14 = 616.
5. Yoo d = 10 ta'e, naannawaan meeqa? (π = 3.14)
Deebii: 31.4Ibsa: 3.14 × 10 = 31.4.
6. Gatiin tilmaamaa π (Pi) meeqa?
Deebii: 3.14 ykn 22/7Ibsa: Kun ratiyoo naannawaafi daayaameetiraati.
7. Yoo r = 1 ta'e, naannawaan meeqa?
Deebii: 2πIbsa: 2 × π × 1 = 2π.
8. Yoo r = 3 ta'e, bal’inni meeqa?
Deebii: 9πIbsa: π × 32 = 9π.
9. Raadiyasiin yoo dachaa (double) guddate, naannawaan harka meeqa guddata?
Deebii: Harka 2Ibsa: Naannawaan raadiyasii waliin qajeelaan (directly) deema.
10. Raadiyasiin yoo dachaa 2 guddate, bal’inni harka meeqa guddata?
Deebii: Harka 4Ibsa: Bal’inni r2 waan ta’eef, 22 = 4.
11. Daayaameetirri geengoo tokkoo 20cm yoo ta’e, r meeqa?
Deebii: 10 cmIbsa: r = d/2 = 20/2 = 10.
12. Naannawaan geengoo tokkoo 88cm yoo ta'e, r meeqa?
Deebii: 14 cmIbsa: 88 = 2 × (22/7) × r → r = (88 × 7) / 44 = 14.
13. Yoo r = 21 ta'e, naannawaan meeqa?
Deebii: 132Ibsa: 2 × (22/7) × 21 = 2 × 22 × 3 = 132.
14. Bal’inni geengoo tokkoo 314 ta'eef r meeqa? (π = 3.14)
Deebii: 10Ibsa: r2 = 314 / 3.14 = 100. √100 = 10.
15. Geengoon raadiyasiin isaa 0 ta'e bal’ina meeqa qaba?
Deebii: 0Ibsa: π × 02 = 0.