Surface Areas and Volumes: Class 10 Maths Chapter 12 Hinglish mein

Jab tak question kuch aur na kahe, lo $\pi =\frac{22}{7}\mathrm{.}$

1. 1
   NumericalEasyNCERT Exercise 12.1, Q1

   Cube ke shape ke teen lakdi ke blocks, har ek ka volume $27\mathrm{c}{\mathrm{m}}^3,$ ek line mein chipka kar ek cuboid banaya gaya hai.

   HintAI se poochho

   Pehle volume se cube ka edge nikaalo.

   1. (a)

      Cuboid ka surface area nikaalo.

      cm²

      Check karo

      Solution dikhao

      Har cube ka edge $=\sqrt[3]{27}=3\mathrm{c}\mathrm{m},$ isliye cuboid 9 cm x 3 cm x 3 cm ka hai.

      $2(27+9+27)=126\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

   2. (b)

      Yeh teen alag cubes ke total surface area se kitna kam hai?

      cm²

      Check karo

      Solution dikhao

      Teen cubes: $3\times 6\times 9=162\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

      $162-126=36\mathrm{c}{\mathrm{m}}^2:$ chaar chhupe faces, har ek $9\mathrm{c}{\mathrm{m}}^2$ ka.

2. 2
   NumericalMediumNCERT Exercise 12.1, Q2

   Ek dairy ke milk vat ka bottom hemispherical hai aur seedhi cylindrical sides same radius ki hain, aur dhakkan nahi hai. Yeh 1.4 m chauda hai aur rim se sabse neeche ke point tak 1.9 m gehra hai. Iske andar tin ki coating karni hai.

   HintAI se poochho

   Gehraai mein hemisphere ka radius bhi shaamil hai. Top khula hai, isliye dhakkan nahi hai.

   1. (a)

      Andar ka surface area nikaalo.

      m²

      Check karo

      Solution dikhao

      $r=0.7\mathrm{m};$ cylinder ki height $h=1.9-0.7=1.2\mathrm{m}\mathrm{.}$

      Andar $=2\pi r^2+2\pi rh=2\pi r(r+h)\mathrm{.}$

      $2\times \frac{22}{7}\times 0.7\times 1.9=8.36{\mathrm{m}}^2\mathrm{.}$

   2. (b)

      Tinning ka kharcha ₹ 250 per m² hai. Kul kharcha nikaalo.

      ₹

      Check karo

      Solution dikhao

      $8.36\times 250=2090,$ yaani ₹ 2090.

3. 3
   NumericalMediumNCERT Exercise 12.1, Q3

   Machhli pakadne ka float radius 1.4 cm ka ek cone hai jo same radius ke hemisphere par laga hai. Float ki kul height 6.2 cm hai. Uska total surface area nikaalo.

   cm²

   Check karo

   HintAI se poochho

   Cone ki height paane ke liye hemisphere ka radius ghatao.

   Solution dikhao

   Cone ki height $=6.2-1.4=4.8\mathrm{c}\mathrm{m};$ $l=\sqrt{1.96+23.04}=5\mathrm{c}\mathrm{m}\mathrm{.}$

   TSA $=2\pi r^2+\pi rl=\pi r(2r+l)\mathrm{.}$

   $\frac{22}{7}\times 1.4\times 7.8=4.4\times 7.8=34.32\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

4. 4
   NumericalMediumNCERT Exercise 12.1, Q4

   Chandan ki lakdi ka ek block, 14 cm × 10 cm × 8 cm, apne 14 cm × 10 cm wale face par rakha hai. Uske top face par ek hemisphere lagana hai.

   HintAI se poochho

   Rectangle par circle tabhi fit hota hai jab uska diameter chhoti side se zyada na ho.

   1. (a)

      Hemisphere zyada se zyada kitna chauda ho sakta hai?

      cm

      Check karo

      Solution dikhao

      Top face 14 cm x 10 cm ka hai, isliye us par sabse bade circle ka diameter 10 cm hai.

   2. (b)

      Us hemisphere ke saath solid ka total surface area nikaalo.

      cm²

      Check karo

      Solution dikhao

      Cuboid: $2(140+80+112)=664\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

      Hemisphere jodta hai $\pi r^2=\frac{22}{7}\times 25\approx 78.57\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

      Kul $\approx 742.57\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

5. 5
   Short answerHardNCERT Exercise 12.1, Q5

   Lakdi ki ek sindoor dibbi ek cube hai jiska edge hai $a\mathrm{.}$ Uske top face ke centre se radius $\frac{a}{4}$ ka ek hemispherical hollow khoda gaya hai.

   HintAI se poochho

   Hollow ek circle hata deta hai aur ek curved andar wala hissa jod deta hai.

   1. (a)

      Dibbi ka surface area is variable ke terms mein nikaalo: $a\mathrm{.}$

      Solution dikhao

      Answer$\frac{a^2}{16}(96+\pi )$

      Cube: $6a^2\mathrm{.}$ Hollow hataata hai $\pi (\frac{a}{4}{)}^2$ aur jodta hai $2\pi (\frac{a}{4}{)}^2,$ yaani net $+\frac{\pi a^2}{16}\mathrm{.}$

      Surface area $=6a^2+\frac{\pi a^2}{16}=\frac{a^2}{16}(96+\pi )\mathrm{.}$

   2. (b)

      Iski value nikaalo jab $a=8\mathrm{c}\mathrm{m}\mathrm{.}$

      cm²

      Check karo

      Solution dikhao

      $\frac{64}{16}(96+\frac{22}{7})=4\times 99.14\approx 396.57\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

6. 6
   NumericalEasyNCERT Exercise 12.1, Q6

   Ghar ka gas cylinder lagbhag ek cylinder hai jiske dono ends par ek-ek hemisphere hai. Yeh kul 70 cm lamba aur 28 cm chauda hai. Valve aur collar ko chhod kar uski bahari surface ka area nikaalo.

   cm²

   Check karo

   HintAI se poochho

   Yeh ek capsule hai: dono ends milkar ek sphere banate hain.

   Solution dikhao

   $r=14\mathrm{c}\mathrm{m};$ cylindrical part ki length hai $70-28=42\mathrm{c}\mathrm{m}$.

   Area $=2\pi r(2r+h)=2\times \frac{22}{7}\times 14\times 70.$

   $=88\times 70=6160\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

7. 7
   NumericalMediumNCERT Exercise 12.1, Q7

   Desert camp ka ek tent 2.5 m uncha aur 7 m chauda cylinder hai, jiske upar slant height 4.5 m ka cone hai. Farsh ke liye canvas use nahi hota.

   HintAI se poochho

   Sirf cylinder ki side aur cone ki curved surface gino.

   1. (a)

      Kitna canvas chahiye, uska area nikaalo.

      m²

      Check karo

      Solution dikhao

      $r=3.5\mathrm{m}\mathrm{.}$ Canvas $=2\pi rh+\pi rl=\pi r(2h+l)\mathrm{.}$

      $\frac{22}{7}\times 3.5\times 9.5=11\times 9.5=104.5{\mathrm{m}}^2\mathrm{.}$

   2. (b)

      Canvas ₹ 240 per m² ka hai. Kul kharcha nikaalo.

      ₹

      Check karo

      Solution dikhao

      $104.5\times 240=25080,$ yaani ₹ 25 080.

8. 8
   NumericalMediumNCERT Exercise 12.1, Q8

   Agarbatti ka stand lakdi ka ek solid cylinder hai, radius 3 cm aur height 10 cm. Uske top mein radius 3 cm aur gehraai 4 cm ka ek conical hollow kaata gaya hai. Stand ka total surface area nikaalo.

   cm²

   Check karo

   HintAI se poochho

   Side, bottom circle aur hollow ka dhalaan wala andar ka hissa gino. Top circle ab nahi raha.

   Solution dikhao

   Hollow ki slant height: $l=\sqrt{9+16}=5\mathrm{c}\mathrm{m}\mathrm{.}$

   TSA $=2\pi rh+\pi r^2+\pi rl=\pi (60+9+15)=84\pi \mathrm{.}$

   $84\times \frac{22}{7}=264\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

9. 9
   NumericalHardNCERT Exercise 12.1, Q9

   Ek carpenter lakdi ka ek solid cylinder banata hai, 14 cm chauda aur 20 cm uncha. Har flat end ke centre se woh 7 cm chauda ek hemisphere khod deta hai. Taiyaar cheez ka total surface area kitna hai?

   cm²

   Check karo

   HintAI se poochho

   Ab har end par ek flat ring aur ek curved hollow hai.

   Solution dikhao

   $R=7\mathrm{c}\mathrm{m},$ $r=3.5\mathrm{c}\mathrm{m}\mathrm{.}$ Side: $2\pi Rh=280\pi \mathrm{.}$

   Dono end rings: $2\pi (R^2-r^2)=2\pi (49-12.25)=73.5\pi \mathrm{.}$

   Dono hollows: $2\times 2\pi r^2=49\pi \mathrm{.}$

   Kul $=402.5\pi =402.5\times \frac{22}{7}=1265\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

10. 10
    Quick answerEasy

    Radius $r$ ka ek hemisphere ek cube ke ek face par laga hai, aur cube ka edge isse bada hai: $2r\mathrm{.}$ Solid ka TSA hai cube ka TSA

    Aplus $2\pi r^2$Bplus $\pi r^2$Cminus $\pi r^2$Dplus $3\pi r^2$

    Check karo

    Answer dekho

    Answer (B) plus $\pi r^2$

    Yeh face ka $\pi r^2$ chhupata hai aur jodta hai $2\pi r^2,$ yaani net $+\pi r^2\mathrm{.}$ $3\pi r^2$ jodna galti se hemisphere ka poora TSA le leta hai.

    HintAI se poochho

    Ek circle dhak jaata hai aur ek curved surface jud jaati hai.

Jab tak question kuch aur na kahe, lo $\pi =\frac{22}{7}\mathrm{.}$

1. 1
   Short answerMediumNCERT Exercise 12.2, Q1

   Lakdi ke ek ghoomne wale toy ka base radius $r$ ka hemisphere hai aur uske flat face par height $2r$ ka cone laga hai. Lo $r=3\mathrm{c}\mathrm{m}\mathrm{.}$

   HintAI se poochho

   Numbers daalne se pehle dono volumes $r$ mein likho.

   1. (a)

      Toy ka volume nikaalo, $\pi$ ko symbol hi rehne do.

      Solution dikhao

      Answer$36\pi \mathrm{c}{\mathrm{m}}^3$

      $\frac{2}{3}\pi r^3+\frac{1}{3}\pi r^2(2r)=\frac{4}{3}\pi r^3\mathrm{.}$

      Jab $r=3:$ $\frac{4}{3}\pi \times 27=36\pi \mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   2. (b)

      Dikhao ki yeh us sphere ke volume ke barabar hai jiska radius hai $r\mathrm{.}$

      Solution dikhao

      $\frac{2}{3}\pi r^3+\frac{2}{3}\pi r^3=\frac{4}{3}\pi r^3,$ yaani sphere ka volume. Height $2r$ wale cone ka volume bilkul gaayab upar wale hemisphere jitna hai.

2. 2
   NumericalMediumNCERT Exercise 12.2, Q2

   Kaagaz ki Diwali lantern (आकाश कंदील) ek cylinder hai jiske dono ends par ek-ek cone hai. Yeh 28 cm chaudi aur kul 60 cm lambi hai, aur har cone 12 cm uncha hai. Iske andar ki hawa ka volume nikaalo.

   cm³

   Check karo

   HintAI se poochho

   Dono cones ke baad jo bachta hai, wahi cylinder ki length hai.

   Solution dikhao

   $r=14\mathrm{c}\mathrm{m};$ cylinder ki length hai $60-24=36\mathrm{c}\mathrm{m}$.

   Cylinder: $\pi r^2\times 36.$ Do cones: $2\times \frac{1}{3}\pi r^2\times 12=\pi r^2\times 8.$

   $V=\frac{22}{7}\times 196\times 44=27104\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

3. 3
   NumericalMediumNCERT Exercise 12.2, Q3

   Patli Diwali candles moulds mein dhaali jaati hain. Har candle 1.4 cm diameter aur 10 cm length ka cylinder hai jiske upar 3 cm height ka cone hai. Girne-bikharne ke liye lagbhag 10% extra wax pighlaya jaata hai. 50 candles ke liye kitna wax pighlana padega?

   cm³

   Check karo

   HintAI se poochho

   Ek candle ka volume nikaalo, 50 se multiply karo, phir 10% jodo.

   Solution dikhao

   $r=0.7\mathrm{c}\mathrm{m}\mathrm{.}$ Ek candle: $\pi r^2(10+\frac{3}{3})=\frac{22}{7}\times 0.49\times 11=16.94\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   50 candles: $847\mathrm{c}{\mathrm{m}}^3\mathrm{.}$ 10% extra ke saath: $847\times 1.1=931.7\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

4. 4
   NumericalMediumNCERT Exercise 12.2, Q4

   Tyohaar ke laddoos ke liye lakdi ki ek tray 21 cm × 14 cm × 4 cm ka cuboid hai. Uske top mein chhe hemispherical hollows khode gaye hain, har ek ka radius 2.1 cm. Tray mein kitni lakdi bachi hai?

   cm³

   Check karo

   HintAI se poochho

   Cuboid mein se chhe hemispheres ghatao.

   Solution dikhao

   Cuboid: $21\times 14\times 4=1176\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   Ek hollow: $\frac{2}{3}\times \frac{22}{7}\times {2.1}^3=19.404\mathrm{c}{\mathrm{m}}^3;$ chhe: $116.424\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   Lakdi $=1176-116.424\approx 1059.58\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

5. 5
   NumericalMediumNCERT Exercise 12.2, Q5

   Purani kahaani ke pyaase kauwe ki tarah, Meena radius 1 cm ke spherical kankad radius 4 cm ke cylindrical matke mein daalti hai, jismein thoda paani bhara hai. Saare kankad doob jaate hain. Kitne kankad paani ko 2.5 cm upar uthayenge?

   Check karo

   HintAI se poochho

   Upar uthe paani ka volume kankadon ke volume ke barabar hai.

   Solution dikhao

   Upar utha paani $=\pi \times 4^2\times 2.5=40\pi \mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   Ek kankad $=\frac{4}{3}\pi \times 1^3=\frac{4}{3}\pi \mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   Number $=40\pi ÷\frac{4}{3}\pi =30.$

6. 6
   NumericalMediumNCERT Exercise 12.2, Q6

   Gym ka ek dumbbell solid iron ka hai: radius 6 cm aur motaai 3 cm ki do barabar discs (cylinders), jo radius 1.5 cm aur length 12 cm ke cylindrical handle se judi hain. Iron ki density lagbhag 7.8 g per cm³ hai. Use karo $\pi =\mathrm{3.14.}$

   HintAI se poochho

   Teen cylinders: unke volumes jodo, phir density se multiply karo.

   1. (a)

      Iron ka volume nikaalo.

      cm³

      Check karo

      Solution dikhao

      Discs: $2\times \pi \times 36\times 3=216\pi \mathrm{.}$ Handle: $\pi \times 2.25\times 12=27\pi \mathrm{.}$

      Kul $=243\pi =763.02\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   2. (b)

      Uska mass kg mein nikaalo, do decimal places tak.

      kg

      Check karo

      Solution dikhao

      $763.02\times 7.8=5951.556\mathrm{g}\approx 5.95\mathrm{k}\mathrm{g}\mathrm{.}$

7. 7
   NumericalHardNCERT Exercise 12.2, Q7

   Radius 35 cm aur height 100 cm ka ek cylindrical drum kinaare tak paani se bhara hai. Ek solid, jo same radius ke hemisphere par ek cylinder (radius 21 cm, height 50 cm) se bana hai, gol end neeche rakh kar andar utaara jaata hai jab tak woh bottom ko na chhoo le, aur paani bahar gir jaata hai. Drum mein kitne litres bachte hain?

   L

   Check karo

   HintAI se poochho

   Agar solid poora paani mein doob jaaye, to bahar gire paani ka volume solid ke volume jitna hota hai.

   Solution dikhao

   Drum: $\frac{22}{7}\times {35}^2\times 100=385000\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   Solid: $\pi r^2(50+\frac{2}{3}\times 21)=\frac{22}{7}\times 441\times 64=88704\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   Yeh 71 cm uncha hai, isliye poora paani mein dooba hai.

   Bacha $=296296\mathrm{c}{\mathrm{m}}^3\approx 296.3\mathrm{L}\mathrm{.}$

8. 8
   NumericalMediumNCERT Exercise 12.2, Q8

   Mitti ki ek surahi ka body sphere ki shape ka hai jiska andar ka diameter 18 cm hai, aur uski cylindrical gardan ka andar ka diameter 4 cm aur length 10 cm hai. Bechne wala kehta hai ki ismein 3.5 litres aata hai. Gardan ko sphere ke upar alag cylinder maan kar iski capacity litres mein, do decimal places tak, nikaalo. Kya bechne wala sahi hai? Use karo $\pi =\mathrm{3.14.}$

   L

   Check karo

   HintAI se poochho

   Ek sphere aur ek cylinder jodo, phir 1000 se divide karo.

   Solution dikhao

   Body: $\frac{4}{3}\times 3.14\times 9^3=3052.08\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   Gardan: $3.14\times 2^2\times 10=125.6\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   Kul $=3177.68\mathrm{c}{\mathrm{m}}^3\approx 3.18\mathrm{L}\mathrm{.}$ 3.5 L ka daawa zyada hai.

9. 9
   Quick answerEasy

   Ek hemispherical hollow, jiska volume $60\mathrm{c}{\mathrm{m}}^3$ hai, ek solid cylinder mein se khoda gaya hai jiska volume hai $500\mathrm{c}{\mathrm{m}}^3\mathrm{.}$ Bache hue solid ka volume hai

   A$560\mathrm{c}{\mathrm{m}}^3$B$500\mathrm{c}{\mathrm{m}}^3$C$440\mathrm{c}{\mathrm{m}}^3$D$380\mathrm{c}{\mathrm{m}}^3$

   Check karo

   Answer dekho

   Answer (C) $440\mathrm{c}{\mathrm{m}}^3$

   Hollow ghatata hai: $500-60=440\mathrm{c}{\mathrm{m}}^3\mathrm{.}$ (Iske ulat, surface area badh jaata hai.)

   HintAI se poochho

   Kya hollow solid mein jagah jodta hai ya ghatata hai?

Jab tak question kuch aur na kahe, lo $\pi =\frac{22}{7}\mathrm{.}$

1. 1
   Quick answerEasy

   Do cubes, har ek ka edge 4 cm, face se face jode gaye hain. Bane hue cuboid ka total surface area hai

   A$192\mathrm{c}{\mathrm{m}}^2$B$160\mathrm{c}{\mathrm{m}}^2$C$128\mathrm{c}{\mathrm{m}}^2$D$176\mathrm{c}{\mathrm{m}}^2$

   Check karo

   Answer dekho

   Answer (B) $160\mathrm{c}{\mathrm{m}}^2$

   Har cube ka hai $96\mathrm{c}{\mathrm{m}}^2;$ jodne se do faces chhup jaate hain: $192-32=160\mathrm{c}{\mathrm{m}}^2\mathrm{.}$ 192 chhupe faces ko bhool jaata hai.

   HintAI se poochho

   $16\mathrm{c}{\mathrm{m}}^2$ ke do faces andar chale jaate hain.

2. 2
   Quick answerEasy

   Radius $r$ aur height $k$ ka ek cone same radius ke cylinder par khada hai, jiski height hai $h\mathrm{.}$ Solid ka volume hai

   A$\pi r^2(h+k)$B$\pi r^2(h+3k)$C$\pi r^2(h+\frac{k}{3})$D$\frac{1}{3}\pi r^2(h+k)$

   Check karo

   Answer dekho

   Answer (C) $\pi r^2(h+\frac{k}{3})$

   $\pi r^{2}h+\frac{1}{3}\pi r^{2}k=\pi r^2(h+\frac{k}{3})\mathrm{.}$

   HintAI se poochho

   Dono volumes jodo aur common nikaalo $\pi r^2\mathrm{.}$

3. 3
   Quick answerMedium

   Ek solid cylinder ka radius $r$ hai aur height $2r,$ aur uske dono ends se radius $r$ ka ek-ek hemisphere khoda gaya hai. Bacha hua volume hai

   A$\frac{2}{3}\pi r^3$B$\frac{4}{3}\pi r^3$C$2\pi r^3$D$\frac{1}{3}\pi r^3$

   Check karo

   Answer dekho

   Answer (A) $\frac{2}{3}\pi r^3$

   $2\pi r^3-\frac{4}{3}\pi r^3=\frac{2}{3}\pi r^3\mathrm{.}$

   HintAI se poochho

   Do hemispheres milkar ek sphere banate hain.

4. 4
   Quick answerEasy

   Assertion (A): Ek cone same radius ke hemisphere par laga hai. Solid ka TSA cone ke CSA plus hemisphere ke CSA ke barabar hai. Reason (R): Jo do flat circular faces jude hain, woh solid ke bahar nahi hain.

   AA aur R dono true hain, aur R, A ka sahi explanation hai.BA aur R dono true hain, lekin R, A ka sahi explanation nahi hai.CA true hai, lekin R false hai.DA false hai, lekin R true hai.

   Check karo

   Answer dekho

   Answer (A) A aur R dono true hain, aur R, A ka sahi explanation hai.

   Dono true hain, aur chhupe flat faces hi wajah hain ki sirf do curved surfaces gini jaati hain.

   HintAI se poochho

   Kya R true hai, aur kya woh A ko explain karta hai?

5. 5
   Quick answerMedium

   Assertion (A): Jab do solids jode jaate hain, to naye solid ka volume unke volumes ke sum se kam hota hai. Reason (R): Jab do solids jode jaate hain, to unki surfaces ka kuch hissa chhup jaata hai.

   AA aur R dono true hain, aur R, A ka sahi explanation hai.BA aur R dono true hain, lekin R, A ka sahi explanation nahi hai.CA true hai, lekin R false hai.DA false hai, lekin R true hai.

   Check karo

   Answer dekho

   Answer (D) A false hai, lekin R true hai.

   Volumes bilkul jud jaate hain, isliye A false hai. R true hai: isi wajah se surface areas seedhe nahi judte.

   HintAI se poochho

   Kya face chhupne se koi jagah hat jaati hai?

6. 6
   Short answerMedium

   Ek solid radius 7 cm aur height 10 cm ka cylinder hai jiske upar same radius aur height 24 cm ka cone hai.

   HintAI se poochho

   Cylinder ka bottom circle ab bhi dikhta hai; uska top circle nahi.

   1. (a)

      Iska total surface area nikaalo.

      cm²

      Check karo

      Solution dikhao

      $l=\sqrt{7^2+{24}^2}=25\mathrm{c}\mathrm{m}\mathrm{.}$

      TSA $=2\pi rh+\pi r^2+\pi rl=\pi (140+49+175)=364\pi \mathrm{.}$

      $364\times \frac{22}{7}=1144\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

   2. (b)

      Iska volume nikaalo.

      cm³

      Check karo

      Solution dikhao

      $\pi r^2(h+\frac{k}{3})=\pi \times 49\times 18=882\pi \mathrm{.}$

      $882\times \frac{22}{7}=2772\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

7. 7
   Long answerHard

   Gaon ki ek water tank radius 3 m aur height 7 m ka cylinder hai, jiska bottom same radius ka hemisphere hai aur dhakkan flat hai. Use karo $\pi =\mathrm{3.14.}$

   HintAI se poochho

   Capacity: cylinder + hemisphere. Paint: sirf do curved surfaces.

   1. (a)

      Iski capacity litres mein nikaalo.

      L

      Check karo

      Solution dikhao

      $V=\pi r^{2}h+\frac{2}{3}\pi r^3=\pi (63+18)=81\pi \mathrm{.}$

      $81\times 3.14=254.34{\mathrm{m}}^3=254340\mathrm{L}\mathrm{.}$

   2. (b)

      Iski curved surfaces ke bahar ₹ 45 per m² ki dar se paint hota hai. Kharcha nikaalo.

      ₹

      Check karo

      Solution dikhao

      Area $=2\pi rh+2\pi r^2=\pi (42+18)=60\pi =188.4{\mathrm{m}}^2\mathrm{.}$

      $188.4\times 45=8478,$ yaani ₹ 8478.

   3. (c)

      Har ghar ek din mein 450 L use karta hai. Ek bhari tank kitne gharon ko ek din ka paani de sakti hai?

      Check karo

      Solution dikhao

      $254340÷450=565.2,$ yaani 565 ghar.

8. 8
   Long answerMedium

   Case study. Ek mithai ki dukaan do gol gulab jamun andar ke radius 4.2 cm wali hemispherical steel ki katori (कटोरी) mein deti hai aur katori ko kinaare tak chaashni se bhar deti hai. Har gulab jamun radius 1.4 cm ka sphere hai.

   HintAI se poochho

   Katori: aadha sphere. Chaashni: katori minus do spheres.

   1. (a)

      Katori ki capacity nikaalo.

      cm³

      Check karo

      Solution dikhao

      $\frac{2}{3}\pi r^3=\frac{2}{3}\times \frac{22}{7}\times {4.2}^3=155.232\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   2. (b)

      Ek serving mein kitni chaashni hai?

      cm³

      Check karo

      Solution dikhao

      Do gulab jamun: $2\times \frac{4}{3}\pi (1.4{)}^3\approx 23.00\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

      Chaashni $\approx 155.23-23.00=132.23\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

   3. (c)

      Katori ke bahar nakkashi ki jaati hai. Uska bahar ka radius bhi 4.2 cm maan kar nakkashi wala area nikaalo.

      cm²

      Check karo

      Solution dikhao

      $2\pi r^2=2\times \frac{22}{7}\times 17.64=110.88\mathrm{c}{\mathrm{m}}^2\mathrm{.}$

   4. (d)

      Chaashni radius 7 cm aur height 20 cm ke cylindrical tin se aati hai. Ek tin se kitni poori servings bhar sakti hain?

      Check karo

      Solution dikhao

      Tin $=\frac{22}{7}\times 49\times 20=3080\mathrm{c}{\mathrm{m}}^3\mathrm{.}$

      $3080÷132.23\approx 23.3,$ yaani 23 poori servings.