Multiple choice

The diameter of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it melted and made of solid cylinder of length 8/3 cm, then the diameter ( in cm ) of the cylinder is : एक खोखले गोले का आन्तरिक और बाह्य का व्यास 6 सेमी और 10 सेमी है यदि इसको पिघलाकर एक ठोस बेलन बनाया जाता है जिसकी लम्बाई 8/3 सेमी है तो ठोस बेलन का व्यास क्या होगा ?

  1. 10

  2. 16

  3. 7

  4. 14
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D Correct answer
Explanation

Volume of hollow sphere = (4/3)π(R³ - r³) = (4/3)π(5³ - 3³) = (4/3)π(98). This becomes volume of cylinder: πr²(8/3). Equating: (4/3)π × 98 = πr²(8/3). Solving: r² = 49, so r = 7 cm and diameter = 14 cm.

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