Thos aakritiyon ke net aur dabbe par sabse chhota raasta
Short mein jawab
Net ek samtal aakaar hai jo modkar thos banta hai. Cube ke 11 alag net hain aur niyamit tetrahedron ke 2. Cylinder ek aayat aur do vritton mein khulta hai, aur cone ek sector aur ek vritt mein. Net dabbe par do binduon ke beech sabse chhota raasta bhi dete hain: kisi sahi net par seedhi rekha.
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Net kya hai?
Dabbe, tin aur cone jaise kai khokhle thos kaagaz, card ya dhaatu ki samtal chaadar modkar bante hain. Jo samtal aakaar modkar thos banta hai wo uska net hai: samtal par ‘khola hua’ thos. Packing ke dabbon mein chipkaane ke liye extra flaps hote hain; ve model banaane mein madad karte hain par net ka hissa nahi. Asli model ke liye card itna kada bhi hona chahiye ki khada rahe.
Cube ke net
Chhe vargon ka cross, yaani chaar ki pankti aur ek varg upar aur ek neeche, modkar cube banta hai. Ye akela net nahi. Agar ghumaakar ya palatkar ek-doosre jaise bante net ek gine jaayein, to cube ke theek 11 net hain: chhe 1–4–1 prakaar ke, teen 2–3–1, ek 3–3 aur ek 2–2–2 seedhi. Aasaan jaanch: agar modte samay do varg ek hi falak par aayein, to wo aakaar net nahi.
Cuboid ka net isi tarah aayaton se banta hai: 5 cm × 3 cm × 1 cm ke dabbe ke liye chaar aayaton ki patti (5 × 3, 5 × 1, 5 × 3, 5 × 1) aur siron par do 3 × 1 ke aayat.
Tetrahedron, cylinder aur cone
Niyamit tetrahedron ke chaar samabahu tribhuj falak hain aur sirf 2 net: chaar ka bana bada tribhuj, aur chaar ki seedhi patti. Square pyramid ka net ek varg hai jiske har taraf ek barabar tribhuj ho. Cylinder ko oonchaai ke saath kaatkar kholo: vakra sateh ek aayat banti hai jo aadhaar ki paridhi 2πr jitna lamba aur oonchaai jitna chauda ho, aur dono gol sire jude hon. Cone ko ek tirchhi rekha par kaatkar kholo: uske aadhaar ki kor ka har bindu nok O se barabar door hai, isliye vakra sateh O ko kendra maanne wale vritt ka sector banti hai, aur aadhaar ke liye ek vritt. Octahedron, do square pyramid aadhaar se jude, ke 11 net hain, aur 12 panchbhujiya falak wale dodecahedron ke 43,380.
Gend alag hai: koi kaagaz ka tukda gole ko bina silvat, khaali jagah ya overlap ke nahi lapet sakta, isliye gole ka koi net nahi.
Keeda aur laddu
Dabbe ki sateh par ek bhookha keeda sirf sateh par chalkar laddu tak pahunchna chahta hai. Samtal sateh par sabse chhota raasta seedhi rekha hai, isliye dabbe ko kholo: dabbe par har raasta net par barabar lambaai ka raasta ban jaata hai. Agar keede ka raasta net par seedhi rekha ban jaaye, to wahi sabse chhota hai; agar net par mud jaaye, to isse seedha raasta maujood hai. Kabhi seedhi rekha net se baahar chali jaati hai, matlab us tarah khola net kaam ka nahi, aur doosra tareeka aazmaana padta hai.
Book ke sabse mushkil udaaharan, 30 cm × 12 cm × 12 cm ke dabbe, mein keeda ek varg sire ke beech mein, upari kinaare se 1 cm neeche baitha hai, aur laddu doosre sire ke beech mein, nichle kinaare se 1 cm upar. Ek tarah kholne par seedha raasta 1 + 30 + 11 = 42 cm hai. Doosri tarah, paanch falakon se guzarte hue, raasta 24 cm aur 32 cm bhujaaon wale samkon tribhuj ka lamba karn ban jaata hai: Baudhayana theorem se d² = 24² + 32² = 1600, isliye d = 40 cm. Chaalaak raasta chhota hai, isiliye har tareeka jaanchna zaroori hai.
Aur: fractal kya hai, thos aakritiyon ko samajhna, chapter ke notes aur NCERT solutions.
Practice karo
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Niyamit tetrahedron ke kitne net hain?
Jawab dekho
Jawab: (b) 2
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Cylinder ki vakra sateh kis aakaar mein khulti hai?
Jawab dekho
Jawab: (c) aayat
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Cone ki vakra sateh kis aakaar mein khulti hai?
Jawab dekho
Jawab: (b) vritt ka sector
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Net par samkon tribhuj ki bhujaayein 24 cm aur 32 cm hon to sabse chhota raasta nikaalo.
Jawab dekho
Jawab: Baudhayana theorem se, d² = 24² + 32² = 576 + 1024 = 1600, isliye d = 40 cm.
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Koi kaagaz ka net gend ko poori tarah kyon nahi lapet sakta?
Jawab dekho
Jawab: Gola har disha mein muda hai, isliye samtal kaagaz use bina silvat, khaali jagah ya overlap ke nahi dhak sakta. Isiliye Prithvi ka har samtal naksha kuch hisson ko kheench deta hai.
Students ke sawal
Thos ka net kya hai?
Net ek samtal aakaar hai jo modkar thos banta hai; ise kuch kinaaron se kaatkar samtal khola hua thos samjho. Model banaate samay chipkaane ke liye flaps jode jaate hain, par ve net ka hissa nahi.
Cube ke kitne net hote hain?
Gyaarah, agar ek-doosre mein ghumaaye ya palte ja sakne wale net ek hi gine jaayein: chhe mein chaar ki pankti aur har taraf ek varg, teen mein do, teen aur ek ki panktiyaan, ek mein teen ki do panktiyaan, aur ek seedhi jaisa.
Net dabbe par sabse chhota raasta dhoondhne mein kaise madad karta hai?
Dabbe par har raasta net par usi lambaai ka raasta ban jaata hai aur ulta bhi. Samtal net par sabse chhota raasta seedhi rekha hai, isliye dabbe ko alag tareekon se kholo, har baar net par rehne wali seedhi rekha kheencho, aur sabse chhoti chuno.
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