Question
Download Solution PDFएक ठोस घनाभाकार डिब्बे की लंबाई, चौड़ाई और ऊँचाई का अनुपात 7 ∶ 5 ∶ 3 है और इसका कुल पृष्ठीय क्षेत्रफल 11502 वर्ग सेमी है। इसकी चौड़ाई कितनी है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
लंबाई : चौड़ाई : ऊँचाई = 7 : 5 : 3
घनाभाकार डिब्बे का कुल पृष्ठीय क्षेत्रफल = 11502 वर्ग सेमी
प्रयुक्त अवधारणा:
घनाभ का कुल पृष्ठीय क्षेत्रफल = 2 (lb + bh + hl)
घनाभाकार डिब्बे की लंबाई, चौड़ाई और ऊँचाई का अनुपात = 7a : 5a : 3a
गणना:
2 (7a × 5a + 5a × 3a + 3a ×7a) = 11502
⇒ (35a2 + 15a2 + 21a2) = 11502 / 2
⇒ 71a2 = 5751
⇒ a2 = 5751/71
⇒ a = √81
⇒ a = 9
इसलिए, घनाभाकार डिब्बे की चौड़ाई 9 × 5 = 45 है
Shortcut Trick
यहाँ, चौड़ाई को 5 से गुणा किया जाता है, तब उत्तर 5 से विभाज्य है; केवल विकल्प 45, 5 से विभाज्य है।
Last updated on Jun 30, 2025
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