Su'aalo Tusaale ah oo Ka Hadlaya Goobo iyo Qaanso
Goobogu waa qaab joomatari oo aasaasi ah oo inta badan lagu barto heerarka kala duwan ee waxbarashada. Fikraddani ma aha oo kaliya mid khuseysa tacliinta laakiin sidoo kale waxay leedahay codsiyo ballaaran oo ku saabsan nolol maalmeedka, sida naqshadeynta dhismaha, injineernimada waddooyinka, iyo xitaa farshaxanka. Maqaalkani wuxuu ka hadli doonaa dhibaatooyin kala duwan oo ku saabsan wareegyada iyo qaansooyinka, iyo sidoo kale xalalkooda.
Fahmidda Goobo iyo Qaanso Wareeg ah
Goobo waa ururinta dhammaan dhibcaha ku yaal diyaarad oo u dhow meel la bixiyay oo loo yaqaan bartamaha goobada. Masaafada u dhaxaysa bartamaha goobada ilaa meel kasta oo ku taal goobada waxaa loo yaqaan radius. Qaanso goobaaban waa qaybta wareegga oo ay ku xiran yihiin laba dhibcood oo ku yaal goobada.
Qaacidooyinka Aasaasiga ah ee aad u Baahan Tahay inaad Ogaato
1. Wareegga Goobo (K):
\[
K = 2 \pi r
\]
halkaas oo \( r \) uu yahay gacanka goobada iyo \( \pi \approx 3.14 \) ama \( \pi \approx \frac{22}{7} \).
2. Bedka Goobo (A):
\[
A = \pi r^2
\]
3. Dhererka Qaansada (lambarrada):
\[
s = \frac{\theta}{360^\circ} \times 2 \pi r
\]
halkaas oo \( \theta \) ay tahay xagasha dhexe ee darajooyin.
4. Aagga Qaybta (L):
\[
L = \frac{\theta}{360^\circ} \times \pi r^2
\]
Su'aalo iyo Doodo Tusaale ah
Su'aal 1aad: Wareegga Goobo
Su'aal:
Goobo waxay leedahay gacan 14 cm ah. Xisaabi wareegga goobada.
Dood:
Isticmaalka qaacidada wareegga goobada:
\[
K = 2 \pi r
\]
Halkee \( r = 14 \) cm,
\[
K = 2 \jeer \frac{22}{7} \jeer 14 = 2 \jeer 22 \jeer 2 = 88 \, \qoraal{cm}
\]
Markaa, wareegga goobada waa 88 cm.
Su'aal 2: Aagga Goobo
Su'aal:
Waxaa la siiyay goobaabo dhexroorkeedu yahay 10 cm. Xisaabi bedka goobada.
Dood:
Marka hore, waxaan helnaa gacanka goobada:
\[
r = \frac{d}{2} = \frac{10}{2} = 5 \, \qoraal{cm}
\]
Iyadoo la isticmaalayo qaacidada aagga goobada:
\[
A = \pi r^2
\]
\[
A = \pi \times 5^2 = \pi \times 25 \qiyaastii 3.14 \times 25 = 78.5 \, \qoraal{cm}^2
\]
Markaa, bedka goobada waa 78.5 cm².
Su'aal 3: Dhererka Qaanso Wareeg ah
Su'aal:
Goobo leh gacan 21 cm ah waxay leedahay qaanso sameysa xagal dhexe oo ah 60°. Waa maxay dhererka qaansada?
Dood:
Iyadoo la isticmaalayo qaacidada dhererka qaansada:
\[
s = \frac{\theta}{360^\circ} \times 2 \pi r
\]
Halkee \( \theta = 60^\circle \) iyo \( r = 21 \, \text{cm} \),
\[
s = \frac{60^\circ}{360^\circ} \jeer 2 \jeer \frac{22}{7} \jeer 21
\]
\[
s = \frac{1}{6} \jeer 2 \jeer \frac{22}{7} \jeer 21
\]
\[
s = \frac{1}{6} \times 132 = 22 \, \text{cm}
\]
Sidaa darteed, dhererka qaansada waa 22 cm.
Su'aal 4: Aagga Qaybta
Su'aal:
Xisaabi bedka qayb ka mid ah goobada oo leh xagal dhexe oo ah 90° iyo gacan 7 cm ah.
Dood:
Isticmaalka qaacidada aagga qaybta:
\[
L = \frac{\theta}{360^\circ} \times \pi r^2
\]
Halkee \( \theta = 90^\circle \) iyo \( r = 7 \, \text{cm} \),
\[
L = \frac{90^\circ}{360^\circ} \times \pi \times 7^2
\]
\[
L = \frac{1}{4} \times \pi \times 49
\]
\[
L = \frac{49 \pi}{4}
\]
\[
L \qiyaastii \frac{49 \times 3.14}{4} \qiyaastii \frac{153.86}{4} \qiyaastii 38.465 \, \qoraal{cm}^2
\]
Markaa, aagga qaybta waa 38.465 cm².
Su'aal 5: Isku-darka Su'aalaha Wareegga iyo Aagga
Su'aal:
Goobo waxay leedahay wareeg dhan 44 cm. Xisaabi bedka goobada.
Dood:
Marka hore, waxaan helnaa gacanka goobada annagoo adeegsanayna qaacidada wareegga:
\[
K = 2 \pi r
\]
Halkee \( K = 44 \, \qoraalka{cm} \),
\[
44 = 2 \jeer \frac{22}{7} \jeer r
\]
\[
44 = \frac{44}{7} \times r
\]
\[
r = \frac{44 \times 7}{44} = 7 \, \text{cm}
\]
Marka xigta, xisaabi bedka goobada:
\[
A = \pi r^2
\]
\[
A = \pi \times 7^2 = \pi \times 49 \qiyaastii 3.14 \times 49 \qiyaastii 153.86 \, \qoraal{cm}^2
\]
Markaa, bedka goobada waa 153.86 cm².
Su'aal 6: Isbarbardhigga Goobo-goobeedyada
Su'aal:
Laba goobood waxay leeyihiin dhuumo 5 cm iyo 10 cm ah siday u kala horreeyaan. Go'aami saamiga wareegga iyo bedka labada goobood.
Dood:
Ku dhawaad:
Goobada koowaad \( r_1 = 5 \, \text{cm} \):
\[
K_1 = 2 \pi r_1 = 2 \pi \times 5 = 10 \pi \, \text{cm}
\]
Goobada labaad \( r_2 = 10 \, \text{cm} \):
\[
K_2 = 2 \pi r_2 = 2 \pi \times 10 = 20 \pi \, \text{cm}
\]
Isbarbardhigga wareega:
\[
\frac{K_1}{K_2} = \frac{10 \pi}{20 \pi} = \frac{1}{2}
\]
Ballaaran:
Wareegga koowaad:
\[
A_1 = \pi r_1^2 = \pi \times 5^2 = 25 \pi \, \qoraal{cm}^2
\]
Wareegga labaad:
\[
A_2 = \pi r_2^2 = \pi \times 10^2 = 100 \pi \, \qoraal{cm}^2
\]
Isbarbardhigga aagga:
\[
\frac{A_1}{A_2} = \frac{25 \pi}{100 \pi} = \frac{1}{4}
\]
Sidaas darteed, saamiga wareegyada labada goobood waa 1:2 saamiga aagaggoodana waa 1:4.
Gabagabo
Fahmidda fikradaha aasaasiga ah iyo qaacidooyinka wareegyada iyo qaansooyinka ayaa lagama maarmaan u ah xallinta dhibaatooyinka joomatari ee kala duwan. Maqaalkani wuxuu soo bandhigayaa dhowr tusaale oo dhibaatooyin iyo doodo ah si loo xoojiyo fahamkaaga ku saabsan agabkan. Dhibaatooyinka ku celcelinta iyo faham qoto dheer ayaa kaa caawin doona inaad fikradahan ku dabaqdo goobo kala duwan oo waxbarasho iyo xaalado nololeed oo dhab ah.
