✅ Pehle Yeh Aata Hai?
Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:
- 72° ka tukda kitne percent hai?
- 40 ka 3/8 kitna hai?
- Angles 100°, 140° aur x° ho to x = ?
Answers dekho
- 72 ÷ 3.6 = 20%
- 40 ÷ 8 × 3 = 15
- x = 360 − 240 = 120°
Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 5 — Pie Chart Kya Hai? ek baar dekh lijiye, phir yahan wapas aaiye.
— 📌 charumam.com
🎬 Kahani: Aisha Ka “Andaaze Wala” Chart
Class monitor Aisha ne 30 classmates se unka pasandeeda naashta poochha: Samosa 12, Momos 9, Pav bhaji 6, Idli 3.
Use project ke liye pie chart banana tha. Usne gola banaya aur aankh se andaaza lagaake tukde kaat diye: samosa ka thoda bada, momos ka thoda chhota…
Teacher ne dekha aur muskuraayin, “Aisha, idli wala tukda to pav bhaji jitna dikh raha hai, jabki idli wale sirf aadhe hain!” 😅
Aisha boli, “Ma’am, par mujhe kaise pata chalega ki har tukda kitna bada ho?” 🤔 Aaj seekhenge pie chart banana, ekdum sahi angles ke saath. 😉
— 📌 charumam.com
📖 Concept: Data Se Gol Chart Tak
Step 1: Table banao aur kul nikaalo
| Naashta | Bachche |
|---|---|
| Samosa | 12 |
| Momos | 9 |
| Pav bhaji | 6 |
| Idli | 3 |
| Kul | 30 |
WHY kul pehle? Pie chart “poore ka hissa” dikhata hai. Poora kitna hai, yeh pata hue bina hissa nahi nikal sakta.
Step 2: Har cheez ka angle nikaalo
$\text{Angle} = \dfrac{\text{Ginti}}{\text{Kul}} \times 360^\circ$
- Samosa = 12/30 × 360 = 144°
- Momos = 9/30 × 360 = 108°
- Pav bhaji = 6/30 × 360 = 72°
- Idli = 3/30 × 360 = 36°
Shortcut: 1 bachcha = 360 ÷ 30 = 12°. Phir har ginti × 12: 12 × 12 = 144, 9 × 12 = 108…
WHY? Yeh direct proportion hai (Post 1): ginti : kul :: angle : 360. Ek bachche ka angle nikaal liya to baaki sab guna se.
Step 3: Percentage diya ho to × 3.6
Agar data pehle se % mein ho, jaise “Cartoon 40%”, to angle = 40 × 3.6 = 144°.
WHY 3.6? 100% = 360°, to 1% = 3.6° (Post 5).
Step 4: Check: jod = 360°
144 + 108 + 72 + 36 = 360° ✅
WHY yeh check? Agar jod 360 nahi aaya, to ya to kul galat liya, ya kisi angle mein galti hai. Chart banaane se pehle hi pakad lo.
Step 5: Ab chart banao (compass + protractor)
- Compass se ek gola banao, centre pe nishaan lagao.
- Centre se upar ki taraf ek radius (seedhi line) khincho. Yeh shuruaat ki line hai.
- Protractor ka centre gole ke centre pe, aur 0 wali line radius pe rakho. 144° pe nishaan lagao aur centre se line khincho. Pehla tukda (samosa) ban gaya.
- Ab nayi line se agla angle 108° naapo. Phir 72°.
- Jo tukda bacha, woh apne aap 36° hona chahiye. Protractor se check karo.
- Har tukde pe naam aur % likho, upar title do.
WHY aakhri tukda check karna? Har baar protractor rakhne mein thodi galti ho sakti hai, jo jud-jud ke badh jaati hai. Aakhri tukda sahi aaya, matlab poora chart sahi.
— 📌 charumam.com
🔐 Deep Concept: Angles Decimal Mein Aayein To Kya Karein?
Har baar numbers itne pyaare nahi hote. Maan lo 7 bachchon mein: 3 ko cricket, 2 ko football, 2 ko kabaddi pasand hai.
| Khel | Exact angle | Round off |
|---|---|---|
| Cricket | 3/7 × 360 ≈ 154.29° | 154° |
| Football | 2/7 × 360 ≈ 102.86° | 103° |
| Kabaddi | 2/7 × 360 ≈ 102.86° | 103° |
| Kul | 360° | 360° ✅ |
Niyam: Nearest degree tak round karo (protractor itna hi naap sakta hai). Phir jod check karo. Agar round karne se jod 359° ya 361° aa jaaye, to sabse bade tukde mein 1° adjust kar do, kyunki wahan farak sabse kam dikhega.
Gehri baat: Pie chart ka kaam “ek nazar mein hissa dikhana” hai. 0.3° ka farak aankh ko dikhta bhi nahi. Isliye rounding se chart ka sach nahi badalta, bas jod 360° bana rehna chahiye.
sirf charumam.com readers ke liye 🔐
✏️ Solved Examples
Example 1 (Easy): TV dekhne walon ka pasandeeda channel: Entertainment 40%, Sports 30%, News 20%, Others 10%. Har tukde ka angle?
Entertainment = 40 × 3.6 = 144°, Sports = 30 × 3.6 = 108°, News = 20 × 3.6 = 72°, Others = 10 × 3.6 = 36°.
WHY sahi hai? 144 + 108 + 72 + 36 = 360 ✅
📌 charumam.com
Example 2 (Medium): 60 students ke school houses: Red 18, Blue 15, Green 12, Yellow 15. Pie chart ke angles?
1 student = 360 ÷ 60 = 6°.
Red = 18 × 6 = 108°, Blue = 15 × 6 = 90°, Green = 12 × 6 = 72°, Yellow = 15 × 6 = 90°.
WHY sahi hai? 108 + 90 + 72 + 90 = 360 ✅. Blue aur Yellow barabar, to tukde bhi barabar.
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Example 3 (NCERT style): 40 students ke grades: A 6, B 14, C 12, D 8. Pie chart banao.
1 student = 360 ÷ 40 = 9°.
A = 6 × 9 = 54°, B = 14 × 9 = 126°, C = 12 × 9 = 108°, D = 8 × 9 = 72°. Jod = 360 ✅
WHY sahi hai? Percentages bhi check karo: 54 ÷ 3.6 = 15%, 126 ÷ 3.6 = 35%, 108 ÷ 3.6 = 30%, 72 ÷ 3.6 = 20%. Jod = 100% ✅
📌 charumam.com
Ab Aisha bhi expert: Andaaza nahi, angle × protractor! Uska samosa wala tukda ab poore 144° ka hai. 🎉
— 📌 charumam.com
🏠 Real Life Mein Pie Chart Banana
- 📊 School project: Mohalle ke 50 gharon mein kaun sa fuel (LPG, bijli, lakdi) use hota hai, uska pie chart.
- 🏪 Dukaan ki bikri: Kirana wale uncle din ki bikri ko daal, chawal, tel, masale mein baantke dekh sakte hain.
- 💡 Bijli ka bill: AC, fridge, pankhe, light ka hissa dikhaake bachat ka plan.
- 🏏 Cricket innings: Runs kitne chaukon, chhakkon aur daud ke aaye, uska chart.
- 💻 Computer pe: Google Sheets mein data daalo, Insert → Chart → Pie, chart apne aap ban jaata hai (Google Docs aur Sheets).
Har jagah wahi kadam: kul → angle → jod check → chart → label.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Kya karein | Kyun |
|---|---|---|
| Data ginti mein diya hai | ✅ (ginti ÷ kul) × 360, ya 1 item ka angle nikaalo | Ginti aur angle direct proportion mein |
| Data % mein diya hai | ✅ % × 3.6 | 1% = 3.6° |
| Angle decimal mein aaya | ✅ Nearest degree, phir jod 360 check | Protractor whole degree naapta hai |
| Ginti ko seedha % maan lena (jab kul 100 nahi) | ❌ Kabhi nahi | % tabhi jab kul 100 ho |
| Aankh se andaaza lagaake tukde | ❌ Nahi | Chhote farak dikhte nahi, chart jhooth bolega |
— 📌 charumam.com
❌→✅ Worked Mistake
Sawaal: 30 bachchon mein se 12 ko samosa pasand hai. Samosa ka angle kya hoga?
❌ Galat: “12 × 3.6 = 43.2°.”
Galti kya hai? × 3.6 sirf percentage pe lagta hai. 12 to bachchon ki ginti hai, percentage nahi. Kul 30 hai, 100 nahi! Check karo: agar saare 30 bachche aise karo to jod 30 × 3.6 = 108° aayega, 360° nahi. ❌
✅ Sahi:
- Angle = 12/30 × 360 = 144°
- Ya pehle %: 12/30 = 40%, phir 40 × 3.6 = 144° ✅
Yaad rakho: Pehle dekho data ginti mein hai ya % mein. Ginti hai to kul se divide karo.
sirf charumam.com pe milenge!
📝 10 MCQs
Q1. Pie chart mein kisi cheez ka angle kaise nikaalte hain?
Solution dekho
Sahi jawab: (b)
- (a) galat: Kul se divide karna bhool gaye, angle 360 se bhi bada aa jaayega.
- (b) sahi: Hissa × poora angle ✅
- (c) galat: Yeh sirf tab sahi jab kul 100 ho.
- (d) galat: Ulta fraction, chhoti cheez ka angle bada aa jaayega.
Q2. 50 students mein se 10 ko chess pasand hai. Chess ka angle?
Solution dekho
Sahi jawab: (c)
- (a) galat: Ginti ko seedha degree maan liya.
- (b) galat: 36° to 10% ka angle hai, yahan 20% hai.
- (c) sahi: 10/50 × 360 = 72° ✅
- (d) galat: 50 to kul hai.
Q3. 15% hisse ka angle kitna hoga?
Solution dekho
Sahi jawab: (b)
- (a) galat: % ko seedha degree maan liya.
- (b) sahi: 15 × 3.6 = 54° ✅
- (c) galat: 36° = 10% hai.
- (d) galat: 15 × 10, galat factor.
Q4. Kul 24 items ke data mein 1 item ka angle kitna hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: 24 to kul hai.
- (b) sahi: 360 ÷ 24 = 15° ✅
- (c) galat: 360 ÷ 36 = 10, galat kul liya.
- (d) galat: 36° = 10%.
Q5. Pie chart banaane ka sabse pehla kadam kya hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: Angle pata hi nahi, to protractor kis cheez ke liye?
- (b) sahi: Kul ke bina koi angle nahi nikal sakta ✅
- (c) galat: Rang aakhir mein.
- (d) galat: Title zaroori hai par pehla kadam nahi.
Q6. Aapne angles nikaale: 100°, 120°, 130°. Jod 350° aaya. Kya karein?
Solution dekho
Sahi jawab: (b)
- (a) galat: 10° ka farak bada hai, chart galat hoga.
- (b) sahi: Jod 360 hona hi chahiye. Kahin galti hai, dhoondo ✅
- (c) galat: Data mein koi naya hissa nahi hai.
- (d) galat: Teeno mein 10 jodne se jod 380 ho jaayega.
Q7. Protractor kis kaam aata hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: Gola compass se banta hai.
- (b) sahi: Protractor (chaanda) se angle naapte hain ✅
- (c) galat: Seedhi line ruler se.
- (d) galat: Area ke liye formula lagta hai.
Q8. 90 students mein se 30 ko kabaddi pasand hai. Kabaddi ka angle?
Solution dekho
Sahi jawab: (b)
- (a) galat: Ginti ko degree maan liya.
- (b) sahi: 30/90 = 1/3, 1/3 × 360 = 120° ✅
- (c) galat: 90 to kul hai.
- (d) galat: 30 × 3.6, ginti ko % maan liya.
Q9. Data 2 : 3 : 4 ke ratio mein hai. Angles kya honge?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 9 hisse, 1 hissa = 40°. 80, 120, 160 ✅
- (b) galat: Jod sirf 90°.
- (c) galat: Ratio ko seedha angle maan liya.
- (d) galat: Jod 360 hai par ratio 3 : 4 : 5 ho gaya.
Q10. Ek pie chart mein 3 students ka tukda 27° hai. 1 student ka angle?
Solution dekho
Sahi jawab: (b)
- (a) galat: 27 ÷ 9, galat divide.
- (b) sahi: 27 ÷ 3 = 9° ✅
- (c) galat: 27° to 3 students ka hai.
- (d) galat: 27 × 3, guna kar diya.
— 📌 charumam.com
❓ FAQs (Bachchon Ke Asli Sawaal)
1. Pehla tukda kahan se shuru karein?
Aam taur pe centre se upar (12 baje ki disha) wali radius se, aur ghadi ki sui ki disha mein. Yeh ek parampara hai, zaroori niyam nahi. Kahin se bhi shuru karo, bas angles sahi hon.
2. Angle decimal mein aaye to?
Nearest degree tak round karo (154.29° → 154°). Phir jod 360° check karo. Farak aaye to sabse bade tukde mein 1° adjust kar do (Deep Concept).
3. Compass nahi hai to gola kaise banayein?
Koi gol cheez, jaise chudi, katori ya bottle ka dhakkan, pencil se trace kar lo. Centre ka nishaan andaaze se lagao ya gole ko fold karke dhoondo.
4. Tukdon ka order kya rakhein?
Saaf dikhne ke liye aksar bade se chhote tukde, ya data jis order mein diya hai usi mein. “Others/Baaki” wala tukda aakhir mein rakhte hain.
5. Kya computer pe pie chart bana sakte hain?
Haan! Google Sheets ya Excel mein data likho, select karo, phir Insert → Chart → Pie. Computer khud angles nikaal deta hai. Par yeh samajhna zaroori hai ki andar woh wahi (ginti ÷ kul) × 360 kar raha hai.
6. Chart pe kya-kya likhna zaroori hai?
(1) Title: chart kis baare mein hai. (2) Har tukde pe naam. (3) Percentage ya ginti. (4) Agar rang use kiye to legend. Bina title ka chart adhoora hai.
— 📌 charumam.com
🏋️ Practice Zone (12 Sawaal)
Q1. Easy 20 students mein se 5 ko badminton pasand hai. Badminton ka angle?
Solution dekho
5/20 × 360 = 1/4 × 360 = 90°.
Q2. Easy 35% hisse ka angle?
Solution dekho
35 × 3.6 = 126°.
Q3. Easy Kul 45 items hain. 1 item ka angle?
Solution dekho
360 ÷ 45 = 8°.
Q4. Easy 1/6 hisse ka angle?
Solution dekho
1/6 × 360 = 60°.
Q5. Medium 72 logon ki pasandeeda drink: Chai 30, Coffee 24, Juice 18. Angles?
Solution dekho
1 vyakti = 360 ÷ 72 = 5°. Chai 150°, Coffee 120°, Juice 90°. Jod 360 ✅
Q6. Medium ₹18,000 ka mahine ka kharcha: Khaana ₹7,500, Kiraya ₹6,000, Baaki ₹4,500. Angles?
Solution dekho
₹18,000 = 360°, to 1° = ₹50. Khaana 7,500 ÷ 50 = 150°, Kiraya 120°, Baaki 90°.
Q7. Medium Data: 45%, 25%, 20%, 10%. Angles?
Solution dekho
162°, 90°, 72°, 36°. Jod 360 ✅
Q8. Medium Chaar cheezein 1 : 2 : 3 : 4 ke ratio mein hain. Pie chart ke angles?
Solution dekho
Kul 10 hisse, 1 hissa = 36°. 36°, 72°, 108°, 144°.
Q9. NCERT style 180 logon se pasandeeda mausam poochha: Garmi 45, Baarish 75, Sardi 60. Pie chart ke angles nikaalo.
Solution dekho
1 vyakti = 360 ÷ 180 = 2°. Garmi 90°, Baarish 150°, Sardi 120°. Jod 360 ✅
Q10. NCERT style Bachchon ka pasandeeda TV channel: Cartoon 40%, Sports 25%, News 15%, Music 20%. Angles?
Solution dekho
Cartoon 144°, Sports 90°, News 54°, Music 72°. Jod = 360° ✅
Q11. NCERT style 48 students ka pasandeeda subject: Maths 12, Science 16, English 8, Hindi 6, Art 6. Angles?
Solution dekho
1 student = 360 ÷ 48 = 7.5°. Maths 90°, Science 120°, English 60°, Hindi 45°, Art 45°. Jod 360 ✅
Q12. NCERT style Ek ghar mein roz 200 litre paani: Nahaana 80, Kapde 40, Khaana-peena 20, Safai 30, Toilet 30. Pie chart ke angles?
Solution dekho
1 litre = 360 ÷ 200 = 1.8°. Nahaana 144°, Kapde 72°, Khaana-peena 36°, Safai 54°, Toilet 54°. Jod 360 ✅
Answer Key — charumam.com exclusive
🧠 HOTS (Sochne Wale Sawaal)
Q1. 9 bachchon mein se 4 ko cricket, 3 ko football aur 2 ko kabaddi pasand hai. Angles nikaalo. Kya round karna padega?
Solution dekho
1 bachcha = 360 ÷ 9 = 40°. Cricket 160°, Football 120°, Kabaddi 80°. Round karne ki zaroorat nahi, kyunki 9, 360 ko poora divide karta hai.
(7 bachche hote to 360 ÷ 7 ≈ 51.43°, tab round karna padta.)
Q2. Aisha kehti hai, “Protractor nahi hai, par main notebook ke kone se 90° wala tukda bana sakti hoon.” Kya yeh sahi hai? Aur kaunse tukde bina protractor ke ban sakte hain?
Solution dekho
Haan. Notebook ka kona 90° (right angle) hota hai. 90° (25%) aur 180° (50%, seedhi line) bina protractor ke ban jaate hain. 90° ko aadha fold karke 45° bhi mil jaata hai. Par 108° jaise angles ke liye protractor chahiye.
Q3. Class A (30 bachche) mein 12 ko samosa pasand hai (144°). Class B (20 bachche) mein 10 ko (180°). Dono classes ka ek combined pie chart banaya. Samosa ka angle kya hoga? Kya yeh 144° aur 180° ka average (162°) hai?
Solution dekho
Combined: samosa = 12 + 10 = 22, kul = 50. Angle = 22/50 × 360 = 158.4°.
162° nahi, kyunki dono classes ka size alag hai. Badi class (A) ka asar zyada hai, isliye jawab 144° ki taraf jhuka hua hai.
Q4. Ek pie chart mein kisi tukde ka angle 18° badh gaya. Uska percentage kitna badha?
Solution dekho
18 ÷ 3.6 = 5%. Matlab us cheez ka hissa poore ka 5% badh gaya (aur baaki tukdon ka milkar 5% ghata, kyunki kul 100% hi rahega).
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🏆 Olympiad Corner
Q1. Pie chart ke chaar tukde x, 2x, 3x aur 4x degree ke hain. Agar survey mein 250 log the, to sabse bade tukde mein kitne log?
Solution dekho
10x = 360 → x = 36°. Sabse bada = 144°. Log = 144/360 × 250 = 0.4 × 250 = 100.
Q2. Tukda A, tukda B ka 3/4 hai. C = 90° aur D = 60°. A aur B ke angles?
Solution dekho
A + B = 360 − 150 = 210. A = 3/4 B → 7/4 B = 210 → B = 120°, A = 90°.
Q3. Ek school mein 1,440 students hain. Pie chart mein 1° kitne students ke barabar hai? Agar ek tukda 75° ka ho to?
Solution dekho
1° = 1,440 ÷ 360 = 4 students. 75° = 75 × 4 = 300 students.
Q4. Ek parivaar ka mahine ka kharcha ₹36,000 hai: Khaana 40%, Kiraya ₹9,000, Padhaai 15%, baaki Bachat. Har ek ka angle aur bachat ki rakam?
Solution dekho
Khaana 40% → 144°. Kiraya = 9,000/36,000 = 25% → 90°. Padhaai 15% → 54°. Bachat = 100 − 40 − 25 − 15 = 20% → 72°.
Bachat = 20% × 36,000 = ₹7,200. Jod 144 + 90 + 54 + 72 = 360 ✅
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💗 CharuMam Motivation
Aisha ka pehla chart galat bana, par usne haar nahi maani. Agli baar protractor uthaya aur ekdum perfect chart banaya. 📐
Seekhna aisa hi hota hai: pehle andaaza, phir tareeka, phir mahaarat. Galti se mat daro, use naapo aur sudhaaro. Thoda focus, roz ki mehnat, aur sabr, aapka har “chart” ek din perfect banega! 🌟
— 📌 charumam.com
🟢 Master Recap
- Kadam 1: Table banao, kul nikaalo.
- Kadam 2: Angle = (ginti ÷ kul) × 360°. Shortcut: 1 item = 360 ÷ kul.
- Data % mein ho to angle = % × 3.6.
- Kadam 3: Saare angles ka jod 360° check karo.
- Kadam 4: Compass se gola, radius, protractor se ek-ek angle, aakhri tukda check.
- Kadam 5: Naam, %, title aur legend likho.
- Decimal angle → nearest degree, jod 360 banaye rakho.
- Ginti ko kabhi seedha × 3.6 mat karo (jab tak kul 100 na ho).
— charumam.com 🎯
👉 Aage Kya?
Ab tak har jagah dono cheezein saath badhti thin: zyada bachche, bada angle. Par socho, agar zyada mazdoor lagao to kaam kam din mein khatam hota hai! Ek badha, doosra ghata. Agle post mein seekhenge inverse proportion! 🔄
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬