Misalin Tambayar Tattaunawa akan Zane-zanen Zane
A fannin lissafi, da'irar siffa ce ta jirgin sama mai ra'ayoyi masu ban sha'awa da za a yi nazari a kansu, ɗaya daga cikinsu shine baka. baka shine ɓangaren gefen da'ira wanda ke tsakanin maki biyu akan da'irar. A cikin wannan labarin, za mu bincika misalai daban-daban na matsaloli da mafita da suka shafi baka.
Fahimtar Asali Game da Zane-zanen Madauwari
Kafin mu ci gaba zuwa ga misalan tambayoyin, yana da mahimmanci mu fara fahimtar wasu mahimman ra'ayoyi:
1. Da'ira:
Da'ira ita ce tarin dukkan maki a cikin jirgin sama wanda yake da nisan da ya yi daidai da wurin tsakiya da aka bayar.
2. Radius (Yatsu):
Radius shine nisan da ke tsakanin tsakiyar da'irar zuwa kowane wuri a gefen da'irar.
3. Diamita:
Diamita ita ce mafi tsayin nisa daga wani wuri a gefen da'ira zuwa wani wuri a gefen da'ira ta tsakiya. Diamita ya ninka radius sau biyu.
4. Baka:
Baka wani ɓangare ne na gefen da'ira. Idan maki A da B suna kan gefen da'ira, to baka AB shine ɓangaren da'irar tsakanin A da B.
Dabarau Masu Alaƙa da Arc of Circles
Domin auna tsawon baka, muna buƙatar fahimtar dabaru da dama:
1. Tsawon Baka (L):
Tsawon baka mai zagaye shine tsawon gefen da'irar da ya haɗa da baka. Tsarin shine:
\[
L = r \times \theta
\]
inda \( r \) shine radius na da'irar kuma \( \theta \) shine kusurwar tsakiya a cikin radians wanda ke haɗuwa da baka.
2. Tsawon Baka a Digiri:
Idan kusurwar tsakiya tana cikin digiri, muna amfani da dabarar:
\[
L = \frac{\theta}{360^\circ} \times 2\pi r
\]
inda \( \theta \) shine kusurwar tsakiya a digiri.
Tambayoyi da Tattaunawa Samfura
Tambaya ta 1: Lissafin Tsawon Baka
Tambaya:
Da'ira tana da radius na santimita 10. Lissafa tsawon baka da aka yi amfani da shi ta kusurwar tsakiya ta digiri 60.
Tattaunawa:
– Radius na da'ira (\( r \)) = 10 cm
– Kusurwar tsakiya (\( \theta \)) = 60°
Amfani da dabarar tsawon baka a digiri:
\[
L = \frac{\theta}{360^\circ} \times 2 \pi r
\]
\[
L = \frac{60^\circ}{360^\circ} \times 2 \pi \times 10 \text{ cm}
\]
\[
L = \frac{1}{6} \times 2 \pi \times 10 \text{ cm}
\]
\[
L = \frac{20\pi}{6} \rubutu{ cm}
\]
\[
L \kimanin 10.47 \rubutu{ cm}
\]
Don haka, tsawon baka yana da kusan 10.47 cm.
Tambaya ta 2: Tantance Kusurwar Tsakiya daga Tsawon Bakan
Tambaya:
Idan aka ba da da'ira mai radius na 14 cm yana da tsawon baka na 22 cm. Kayyade kusurwar tsakiya da ke haɗa baka a digiri.
Tattaunawa:
– Radius na da'ira (\( r \)) = 14 cm
– Tsawon baka (\( L \)) = 22 cm
Yi amfani da dabarar tsawon baka don nemo \( \theta \):
\[
L = \frac{\theta}{360^\circ} \times 2 \pi r
\]
Maye gurbin dabi'un da aka sani:
\[
22 = \frac{\theta}{360^\circ} \sau 2 \pi \sau 14
\]
Warewa \( \theta \):
\[
22 = \frac{\theta}{360^\circ} \times 28 \pi
\]
\[
22 \sau 360^\circ = \theta \sau 28 \pi
\]
\[
7920 = \theta \times 28 \pi
\]
\[
\theta = \frac{7920}{28 \pi}
\]
\[
\theta \kimanin 90.72^\circa
\]
Don haka, girman kusurwar tsakiya yana da kusan digiri 90.72.
Tambaya ta 3: Lissafin Yankin Sashe
Tambaya:
Ana samar da sashen da'ira ta hanyar kusurwar tsakiya ta digiri 120 tare da radius na santimita 7. Kayyade yankin ɓangaren.
Tattaunawa:
– Radius na da'ira (\( r \)) = 7 cm
– Kusurwar tsakiya (\( \theta \)) = 120°
Yi amfani da dabarar da za a yi amfani da ita don fannin wani fanni:
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
Maye gurbin dabi'un da aka sani:
\[
A = \frac{120^\circ}{360^\circ} \times \pi \times 7^2
\]
\[
A = \frac{1}{3} \times \pi \times 49
\]
\[
A = \frac{49\pi}{3}
\]
\[
A \kimanin 51.43 \rubutu{ cm}^2
\]
Don haka, yankin ɓangaren yana da kusan 51.43 cm².
Tambaya ta 4: Tantance Layin daga Yankin Sashe
Tambaya:
Faɗin ɓangaren da'ira mai radius na 6 cm² shine 18π cm². Menene tsawon baka na ɓangaren?
Tattaunawa:
– Radius na da'ira (\( r \)) = 6 cm
– Yankin ɓangaren (\( A \)) = 18π cm²
Yi amfani da dabarar yanki don wani sashe don nemo kusurwar tsakiya \( \theta \):
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
Maye gurbin dabi'un da aka sani:
\[
18\pi = \frac{\theta}{360^\circ} \times \pi \times 6^2
\]
\[
18\pi = \frac{\theta}{360^\circ} \times 36\pi
\]
\[
18 = \frac{\theta}{360^\circ} \sau 36
\]
\[
Sau 18 360^\cir = \theta \sau 36
\]
\[
6480 = \theta \times 36
\]
\[
\theta = \frac{6480}{36}
\]
\[
\theta = 180^\da'ira
\]
Yanzu, tare da kusurwar tsakiya ta digiri 180, mun ƙayyade tsawon baka:
\[
L = \frac{\theta}{360^\circ} \times 2 \pi r
\]
\[
L = \frac{180^\circ}{360^\circ} \sau 2 \pi \sau 6
\]
\[
L = \frac{1}{2} \sau 2 \pi \sau 6
\]
\[
L = \pi \sau 6
\]
\[
L \kimanin 18.85 \rubutu{ cm}
\]
Don haka, tsawon baka yana da kusan 18.85 cm.
Kammalawa
Fahimtar baka mai zagaye da yadda ake ƙididdige su muhimmin tushe ne a fannin lissafi da lissafi gabaɗaya. Ta hanyar misalan da aka tattauna a cikin wannan labarin, ana sa ran masu karatu za su sami fahimtar yadda ake ƙididdige tsawon baka, yankin sashe, da kuma ƙayyade kusurwar tsakiya da ke haɗa baka. Fahimtar waɗannan mahimman ra'ayoyi zai taimaka sosai wajen magance matsaloli daban-daban da suka shafi da'irori.
