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| source: ncert_exercises |
| topic: geometry |
| class_level: class_9 |
| chapter: ch11 |
| exercise: ex11.4 |
| difficulty: intermediate |
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| Class 9 | Ch11: Surface Areas and Volumes | Exercise 11.4 (Volume of Sphere) |
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| Key Formulas: |
| Sphere: V=(4/3)πr³. Hemisphere: V=(2/3)πr³. |
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| Q1. Find volume of sphere with: (i) r=7 cm (ii) r=0.63 m. |
| Answer: |
| (i) V=4/3×22/7×343=1437.33 cm³. ✅ |
| (ii) V=4/3×22/7×0.250047=1.0478 m³. ✅ |
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| Q2. Find amount of water displaced by spherical ball of: (i) diameter=28 cm (ii) diameter=0.21 m. |
| Answer: V=volume of sphere. |
| (i) r=14. V=4/3×22/7×2744=11498.67 cm³. ✅ |
| (ii) r=0.105. V=4/3×22/7×0.001157625=0.00485 m³=4.85 L. ✅ |
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| Q3. Metal sphere of radius 4.2 cm is melted and recast as small spheres of radius 0.3 cm. Find number. |
| Answer: V_large=4/3×π×4.2³=4/3×π×74.088. V_small=4/3×π×0.3³=4/3×π×0.027. n=74.088/0.027=2744. ✅ |
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| Q4. Depth of a pond=4.5 m, cylindrical pit (r=1.4 m) dug. How much soil is extracted? |
| Answer: This seems to be a cylinder problem. V=πr²h=22/7×1.96×4.5=27.72 m³. ✅ |
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| Q5. Width and depth of river is 40 m and 5 m. River flows at 2 km/hr. Find water that runs into sea per minute. |
| Answer: Volume per minute=width×depth×speed=(40×5×2000/60)=6666.67 m³/min. ✅ |
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| Q6. Marbles of diameter 1.4 cm dropped into cylindrical beaker of diameter 7 cm. How many marbles to raise water by 5.6 cm? |
| Answer: Volume of water raised=π×3.5²×5.6=22/7×12.25×5.6=215.6 cm³. Volume each marble=4/3×π×0.7³=4/3×22/7×0.343=1.4373 cm³. n=215.6/1.4373≈150. ✅ |
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| Q7. Iron sphere of radius 1.5 cm has density 8000 kg/m³. Find mass. |
| Answer: V=4/3×π×1.5³×10⁻⁶ m³=4/3×π×3.375×10⁻⁶=14.137×10⁻⁶ m³. Mass=V×ρ=14.137×10⁻⁶×8000=0.113 kg=113.1 g. ✅ |
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| Q8. Hemispherical bowl is made of steel 0.25 cm thick. Inner radius=5 cm. Find volume of steel. |
| Answer: Outer radius=5.25 cm. V=2/3×π×(5.25³-5³)=2/3×π×(144.703-125)=2/3×π×19.703=41.28 cm³. ✅ |
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| Q9. Hemisphere of radius 1 cm is exactly half of a sphere. Volume=? |
| Answer: V=(2/3)×π×1³=(2/3)π cm³. ✅ |
