Multiple choice

If a metallic cone of radius 30 cm. and height 45 cm. is melted and recast into metallic sphere of radius 5cm., find the number of spheres. यदि 30 सेमी.त्रिज्या और 45 सेमी. ऊँचाई वाले एक शंकु को पिघलाकर 5 सेमी. त्रिज्या वाले गोलों में पुनः ढाला जाए तो गोलों की संख्या ज्ञात कीजिए।

  1. 405

  2. 91

  3. 80

  4. 81
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D Correct answer
Explanation

Volume of cone = (1/3)πr²h = (1/3)π(30)²(45) = (1/3)π(900)(45) = 13500π cm³. Volume of each sphere = (4/3)πr³ = (4/3)π(5)³ = (4/3)π(125) = 500π/3 cm³. Number of spheres = Volume of cone / Volume of sphere = 13500π / (500π/3) = 13500π × (3/500π) = 13500 × 3 / 500 = 81 spheres. The π cancels out and we get exactly 81.

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