Multiple choice

Ratio between curved surface area and total surface area of a circular cylinder is 3 : 5. If curved surface area is 1848 cm2 then what is the height of cylinder. एक बेलन के वक्र पृष्ठीय क्षेत्रफल और कुल पृष्ठीय क्षेत्रफल का अनुपात 3 : 5 है। यदि वक्र पृष्ठीय क्षेत्रफल 1848 सेमी2 है तो बेलन की ऊँचाई क्या है।

  1. 21

  2. 10.5

  3. 42

  4. 11

  5. 15
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A Correct answer
Explanation

For a cylinder, CSA : TSA = 2πrh : 2πr(r + h) = 3 : 5. This means 2πrh / [2πr(r + h)] = 3/5, which simplifies to h / (r + h) = 3/5. Cross-multiplying: 5h = 3r + 3h, so 2h = 3r, giving h = 1.5r or r = (2/3)h. Also, CSA = 2πrh = 1848, so 2πr(1.5r) = 1848. With r = 14, we get h = 1.5 × 14 = 21 cm.

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