Multiple choice

The total surface area of a solid right circular cylinder is twice that of a solid sphere. If they have the same radii,what will be the ratio of the volume of cylinder to that of the sphere. एक ठोस लम्बवृत्तीय बेलन के सम्पूर्ण पृष्ठ का क्षेत्रफल एक ठोस गोले के सम्पूर्ण पृष्ठ के क्षेत्रफल का दोगुना है। यदि उनकी त्रिज्यायें बराबर है तो बेलन के आयतन और गोले के आयतन का अनुपात क्या होगा?

  1. 3 : 2

  2. 9 : 4

  3. 1 : 2

  4. 1 : 4
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B Correct answer
Explanation

Cylinder surface area = 2πr(r+h), sphere surface area = 4πr². Given cylinder SA = 2 × sphere SA, so 2πr(r+h) = 8πr², giving r+h = 4r and h = 3r. Volume of cylinder = πr²h = 3πr³. Volume of sphere = (4/3)πr³. Ratio = 3πr³ : (4/3)πr³ = 9 : 4. 1:2 would be if heights were equal; 3:2 incorrectly uses diameter.

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