Nets: Kaagaz Se Solid | Class 8 Maths Book 2 Ch 4

📘 Class 8 · Ganita Prakash Book 2Ch 4 · Exploring Some Geometric ThemesPost 6 / 9⏱ 25–30 min

Nets: Kaagaz Se Solid ✂️

IS POST MEIN

Pehle Yeh Aata Hai?Kahani Concept Deep Concept Examples Real Life Galti 10 MCQs FAQs Practice HOTS Olympiad Recap

✅ Pehle Yeh Aata Hai?

Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:

Cube ke kitne faces?
Circle ki paridhi (circumference) ka formula?
Cone ka aadhar kaisa?

Answers dekho

6 (sab square)
2πr
Circle

Teeno sahi? Badhiya! Faces-edges yaad karne ho to Post 5 dekh lijiye.

— 📌 charumam.com

🎬 Kahani: Mithai Ka Dabba Kholo

Diwali ki mithai ka dabba khaali hua to Priya ne use dhyaan se khola: chipke hue flaps ukhaade, kinaare khole… aur dabba ek sapaat kaagaz ban gaya, ek ajeeb plus jaisi shape mein!

“Iska ulta karo to dabba phir ban jaata hai,” Golu bola. “Kya har aisi shape se dabba banta hai?”

Priya ne 6 square ek line mein (2 × 3) kaate aur modne ki koshish ki… dabba nahi bana! 😮 To kaun si shapes banti hain? Inhe kehte hain nets. 📦

— 📌 charumam.com

📖 Concept: Modo To Solid, Kholo To Net

Step 1: Net kya hai?

Net ek sapaat (2D) shape hai jise mod ke ek solid (3D) banta hai. Asli dabbe mein chipkaane ke liye flaps hote hain, par net mein flaps nahi gine jaate.

Plus jaisi shape mudke cube banti hai; 2 × 3 wali nahi.

Step 2: Cube ke 11 nets

6 squares ko jodne ke kai tareeke hain, par sirf 11 se cube banta hai (ghumaana ya palatna same maana jaata hai). Jaise 2 × 3 rectangle mein do faces ek doosre pe aa jaate hain aur ek taraf khaali reh jaata hai.

WHY check kaise? Ek square ko neeche (base) maano, aur dimaag mein baaki ko upar modo. Koi do square ek hi jagah aaye ya koi jagah khaali reh jaaye to net nahi.

Step 3: Cuboid ka net

Cuboid 5 cm × 3 cm × 1 cm: 6 rectangles, teen jodi: 5 × 3 (do), 5 × 1 (do), 3 × 1 (do). Jo sides milti hain unki lambaai barabar honi chahiye.

Step 4: Cylinder ka net

Do circles (upar-neeche) + ek rectangle. Rectangle ki ek side = oonchaai h, doosri = circle ki paridhi 2πr.

WHY 2πr? Rectangle ko lapet ke circle ke kinare pe chipkaana hai, to uski lambaai paridhi jitni honi chahiye.

Step 5: Cone ka net

Cone ko ek seedhi line (sire se aadhar tak) pe kaat ke kholo: ek circle ka sector (pankhe jaisa tukda) milta hai, jiska kendra O = cone ki nok. Sector ke chaap (arc) ki lambaai = aadhar ki paridhi 2πr. Saath mein aadhar ka circle.

Step 6: Aur solids

Regular tetrahedron (4 equilateral triangles): sirf 2 nets (ek bada triangle jiske beech ke points jode, aur ek patti jaisa).
Square pyramid: ek square + 4 triangles uski sides pe.
Triangular prism: 2 triangles + 3 rectangles.
Octahedron (8 equilateral triangles, do square pyramids aadhar se jude): 11 nets.
Dodecahedron (12 regular pentagons): 43,380 nets!

— 📌 charumam.com

🔐 Deep Concept: Gend (Sphere) Ka Net Kyun Nahi?

Koshish karo: kaagaz se ek gend ko bina silvat (wrinkle), bina khaali jagah aur bina overlap ke lapet ke dikhao. Nahi hota!

Gend har taraf mudi hui hai, aur sapaat kaagaz ko bina khinche ya sikode is tarah moda nahi ja sakta. Isliye duniya ka naksha (map) hamesha kahin na kahin kheencha hua hota hai: Greenland asli se bahut bada dikhta hai! 🌍 Football bhi pentagon-hexagon ke tukdon se “lagbhag gol” banti hai. 🔐

sirf charumam.com readers ke liye 🔐

✏️ Solved Examples

Example 1 (Easy): Plus (+) jaisi shape jisme beech wale square ke chaaron taraf ek-ek square aur neeche ek aur. Kya yeh cube ka net hai?

Beech wala = base, chaar taraf ke = 4 deewarein, neeche wale ke neeche ka = dhakkan. Haan.

WHY sahi hai? Har face ek baar, koi overlap nahi ✅

📌 charumam.com

Example 2 (Medium): Cylinder r = 7 cm, h = 10 cm. Net ke rectangle ka naap? (π = 22/7)

Lambaai = 2πr = 2 × 22/7 × 7 = 44 cm, chaudaai = 10 cm.

WHY sahi hai? 44 cm ka kaagaz 7 cm radius ke circle ke charon taraf poora lipat ta hai ✅

📌 charumam.com

Example 3 (NCERT style): Cuboid 6 cm × 3 cm × 2 cm ke net mein kaun-kaun se rectangles?

Do 6 × 3, do 6 × 2, do 3 × 2. Kul area = 2(18 + 12 + 6) = 72 cm².

WHY sahi hai? Har jodi aamne-saamne ke faces ✅

📌 charumam.com

Priya ki trick: “Ek square base banao, baaki ko dimaag mein modo!” 🎉

— 📌 charumam.com

🏠 Real Life Mein

📦 Gatte ke dabbe: factory mein net jaisa sapaat kaagaz kaat ke mod ke banaate hain.
🥫 Dabba (tin can) ka label: rectangle hai, lambaai = paridhi.
🍦 Ice-cream cone: sector se banta hai.
🎲 Paasa (dice): cube; net pe aamne-saamne ke number jod 7.

— 📌 charumam.com

🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
6 square, mod ke check	✅ Cube net (11 mein se ek?)	Overlap nahi, gap nahi
2 × 3 ya 1 line mein 6 square	❌ Cube net nahi	Overlap ya khaali face
Cylinder rectangle	✅ h × 2πr	Lapetne ke liye paridhi
Sphere	❌ Net nahi	Bina khinche sapaat nahi hota

— 📌 charumam.com

❌→✅ Worked Mistake

Sawaal: Cylinder r = 3.5 cm, h = 10 cm. Net ka rectangle?

❌ Galat: “10 cm × 3.5 cm (oonchaai × radius).”

Galti kya hai? 3.5 cm ka kaagaz circle ke charon taraf lipat hi nahi sakta ❌

✅ Sahi: Lambaai = 2πr = 2 × 22/7 × 3.5 = 22 cm. Rectangle = 22 cm × 10 cm.

Yaad rakho: Lapetne wali side = paridhi.

sirf charumam.com pe milenge!

📝 10 MCQs

Q1. Net kya hai?

(a) 3D model

(b) Sapaat shape jo mudke solid bane

(c) Solid ka vazan

(d) Ek circle

Solution dekho

Sahi jawab: (b)

(a) galat: Net 2D hai.
(b) sahi: Sahi ✅
(c) galat: Nahi.
(d) galat: Nahi.

Q2. Cube ke kitne alag nets?

(a) 6

(b) 8

(c) 11

(d) 20

Solution dekho

Sahi jawab: (c)

(a) galat: Kam.
(b) galat: Kam.
(c) sahi: 11 ✅
(d) galat: Zyada.

Q3. Cylinder ke net mein rectangle ki lambaai?

(a) r

(b) 2r

(c) 2πr

(d) πr²

Solution dekho

Sahi jawab: (c)

(a) galat: Chhota.
(b) galat: Diameter.
(c) sahi: Paridhi ✅
(d) galat: Area.

Q4. Cone ka net?

(a) Rectangle + circle

(b) Sector + circle

(c) Do triangles

(d) Square

Solution dekho

Sahi jawab: (b)

(a) galat: Cylinder.
(b) sahi: Sahi ✅
(c) galat: Nahi.
(d) galat: Nahi.

Q5. Regular tetrahedron ke nets?

(a) 1

(b) 2

(c) 4

(d) 11

Solution dekho

Sahi jawab: (b)

(a) galat: Kam.
(b) sahi: Sirf 2 ✅
(c) galat: Nahi.
(d) galat: Cube/octahedron.

Q6. Kaun sa solid net se nahi banta?

(a) Cube

(b) Cone

(c) Sphere

(d) Prism

Solution dekho

Sahi jawab: (c)

(a) galat: Banta.
(b) galat: Banta.
(c) sahi: Sapaat nahi hota ✅
(d) galat: Banta.

Q7. Triangular prism ke net mein?

(a) 2 triangles + 3 rectangles

(b) 3 triangles + 2 rectangles

(c) 4 triangles

(d) 6 squares

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Ulta.
(c) galat: Tetrahedron.
(d) galat: Cube.

Q8. Octahedron ke nets?

(a) 2

(b) 8

(c) 11

(d) 43380

Solution dekho

Sahi jawab: (c)

(a) galat: Tetrahedron.
(b) galat: Nahi.
(c) sahi: 11 ✅
(d) galat: Dodecahedron.

Q9. r = 7, π = 22/7: 2πr?

(a) 22

(b) 44

(c) 154

(d) 14

Solution dekho

Sahi jawab: (b)

(a) galat: πr.
(b) sahi: Sahi ✅
(c) galat: πr².
(d) galat: Diameter.

Q10. Cuboid 5 × 3 × 1 ke net mein 5 × 3 wale kitne?

(a) 1

(b) 2

(c) 3

(d) 6

Solution dekho

Sahi jawab: (b)

(a) galat: Aamne-saamne do.
(b) sahi: Sahi ✅
(c) galat: Nahi.
(d) galat: Kul faces.

— 📌 charumam.com

❓ FAQs (Bachchon Ke Asli Sawaal)

1. Flaps net mein kyun nahi gine?

Flaps sirf chipkaane ke liye hain; shape ka hissa nahi.

2. 11 nets kaise dhoondhein?

6 squares ki alag-alag jamaavat kaagaz pe banao, kaato aur modo. Ghumaai/palti hui ko same gino.

3. Cone ka sector bada-chhota kyun?

Sector ka kona cone ki oonchaai aur aadhar pe nirbhar. Chaap = 2πr hona zaroori.

4. Agar O sector ka kendra na ho?

Moda gaya aakaar asli cone nahi banega, kinara seedha nahi milega. Model bana ke dekho!

5. Dice ke net pe kya dhyaan?

Aamne-saamne ke faces ka jod 7 (1–6, 2–5, 3–4).

6. Sphere ka “lagbhag” net?

Football jaise pentagon-hexagon ya globe ke patte, par poora sahi nahi.

— 📌 charumam.com

🏋️ Practice Zone (12 Sawaal)

Q1. Easy Cube net ke kitne squares?

Solution dekho

Q2. Easy Cylinder net mein kitne circles?

Solution dekho

Q3. Easy Square pyramid ke net mein triangles?

Solution dekho

Q4. Easy Cone net ke hisse?

Solution dekho

Sector + circle.

Q5. Medium Cylinder r = 14 cm, h = 5 cm: rectangle?

Solution dekho

88 cm × 5 cm.

Q6. Medium Cuboid 5 × 3 × 1 ke net ka area?

Solution dekho

2(15 + 5 + 3) = 46 cm².

Q7. Medium Cube side 4 cm, net area?

Solution dekho

6 × 16 = 96 cm².

Q8. NCERT style Cuboid 5 cm × 3 cm × 1 cm ka net draw karo.

Solution dekho

Do 5×3, do 5×1, do 3×1 ko is tarah jodo ki milti sides barabar hon.

Q9. NCERT style Regular tetrahedron ka ek net draw karo (side 5 cm).

Solution dekho

Ek bada triangle (side 10 cm), sides ke midpoints jodo → 4 triangles.

Q10. NCERT style Triangular prism ka net (triangle side 3 cm, lambaai 8 cm).

Solution dekho

2 equilateral triangles (3 cm) + 3 rectangles 8 × 3.

Q11. Medium Cone ke net mein sector ka chaap, agar aadhar r = 7 cm?

Solution dekho

44 cm.

Q12. Medium 1 line mein 6 squares, cube banega?

Solution dekho

Nahi (do faces overlap, do khaali).

— 📌 charumam.com

🧠 HOTS (Sochne Wale Sawaal)

Q1. Dice ke net pe 1 ke saamne kaunsa number?

Solution dekho

6 (jod 7).

Q2. Net: 4 squares ek line mein, ek square pehle wale ke upar, ek aakhri wale ke neeche. Cube banega?

Solution dekho

Haan, yeh 1-4-1 type ka net hai (line ke dono taraf ek-ek square, kahin bhi).

Q3. Cylinder ka label ka area?

Solution dekho

2πrh (rectangle ka area).

Q4. Kya 7 squares se cube net ban sakta hai?

Solution dekho

Nahi, cube ke sirf 6 faces.

sirf charumam.com pe milenge!

🏆 Olympiad Corner

Q1. Cube ke 11 nets mein kitne mein 4 squares ek line mein?

Solution dekho

6 nets (1-4-1 wale).

Q2. Cylinder r = 7, h = 10 ke net ka kul area (π = 22/7)?

Solution dekho

Rectangle 440 + do circles 2 × 154 = 748 cm².

Q3. Sector ka angle, agar cone ki tirchhi lambaai 14 cm aur r = 7 cm?

Solution dekho

Chaap 44 = (θ/360) × 2π × 14 = (θ/360) × 88 → θ = 180° (aadha circle).

Q4. A4 kaagaz ki lambi side 29.7 cm ko cylinder ki paridhi banaayein to r kitna? (π ≈ 3.14)

Solution dekho

2πr = 29.7 → r ≈ 29.7 ÷ 6.28 ≈ 4.73 cm.

sirf charumam.com readers ke liye 🔐

💗 CharuMam Motivation

Priya ne mithai ka dabba phenkne se pehle khol ke dekha, aur ganit seekh liya! 📦

Har cheez ke andar ek design chhupa hai. Jigyasa (curiosity) se dekho, “yeh bana kaise?” poochho. Wahi sawaal aapko engineer, designer ya scientist banaayega! ✨

— 📌 charumam.com

🟢 Master Recap

Net: sapaat shape jo mudke solid bane (flaps nahi gine).
Cube: 11 nets; 2 × 3 ya line wale nahi.
Cuboid: 3 jodi rectangles.
Cylinder: 2 circles + rectangle (h × 2πr).
Cone: sector (chaap 2πr) + circle.
Tetrahedron 2 nets, octahedron 11, dodecahedron 43,380. Sphere ka net nahi.

— charumam.com 🎯

👉 Aage Kya?

Nets ka ek mazedaar istemaal: cheenti ko dabbe ki sataha pe laddoo tak sabse chhota raasta dhoondhna! 🐜

← Pichla: Post 5 — Faces, Edges, Vertices: Prism Aur Pyramid 📚 Chapter 4 ke saare posts Agla: Post 7 — Cuboid Pe Sabse Chhota Raasta →

Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Mithai Ka Dabba Kholo

📖 Concept: Modo To Solid, Kholo To Net

Step 1: Net kya hai?

Step 2: Cube ke 11 nets

Step 3: Cuboid ka net

Step 4: Cylinder ka net

Step 5: Cone ka net

Step 6: Aur solids

🔐 Deep Concept: Gend (Sphere) Ka Net Kyun Nahi?

✏️ Solved Examples

🏠 Real Life Mein

🧭 Kab Use Karein, Kab Nahi

❌→✅ Worked Mistake

📝 10 MCQs

❓ FAQs (Bachchon Ke Asli Sawaal)

🏋️ Practice Zone (12 Sawaal)

🧠 HOTS (Sochne Wale Sawaal)

🏆 Olympiad Corner

💗 CharuMam Motivation

🟢 Master Recap

👉 Aage Kya?

You may also like