Question
Download Solution PDFएक घन का पृष्ठीय क्षेत्रफल 5400 वर्ग इकाई है। यदि इसकी भुजा 5 इकाई बढ़ा दी जाए तो इसका आयतन लगभग ______ बढ़ जाएगा।
Answer (Detailed Solution Below)
Detailed Solution
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घन का पृष्ठीय क्षेत्रफल = 5400 वर्ग इकाई
भुजा वृद्धि = 5 इकाई
प्रयुक्त सूत्र:
घन का पृष्ठीय क्षेत्रफल = 6a2
घन का आयतन = a3
गणना:
माना कि घन की भुजा a इकाई है।
पृष्ठीय क्षेत्रफल = 6a2
⇒ 6a 2 = 5400
⇒ a2 = 5400 / 6
⇒ a2 = 900
⇒ a = 30 इकाई
घन की नई भुजा = a + 5 = 30 + 5 = 35 इकाई
मूल आयतन = a 3 = 30 3
⇒ 303 = 27000 घन इकाई
नया आयतन = (a + 5)3 = 353
⇒ 353 = 42875 घन इकाई
आयतन में वृद्धि = नया आयतन - मूल आयतन
⇒ आयतन में वृद्धि = 42875 - 27000
⇒ आयतन में वृद्धि = 15875 घन इकाई
आयतन में अनुमानित वृद्धि = 0.59 x 27000
⇒ 15870 घन इकाई
आयतन लगभग 59% बढ़ जाएगा।
Last updated on Jun 30, 2025
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