Question
Download Solution PDF3 ∶ 4 ∶ 5 के अनुपात वाली भुजाओं वाले तीन घनों को पिघलाकर एक एकल घन बनाया जाता है जिसका विकर्ण 18√3 cm है। तीनों घनों की भुजाएँ कौन-सी हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
3 ∶ 4 ∶ 5 के अनुपात वाली भुजाओं वाले तीन घनों को पिघलाकर एक एकल घन बनाया जाता है जिसका विकर्ण 18√3 cm है।
प्रयुक्त अवधारणा:
घन का विकर्ण = √3a (a भुजा हैं)
गणना:
माना कि घनों की भुजाएँ 3x cm, 4x cm और 5x cm हैं।
प्रश्नानुसार,
नए घन का आयतन निम्न है
(3x)3 +( 4x)3 +( 5x)3 = 216 x3
⇒ भुजा = 6x
विकर्ण 6x√3 है।
⇒ 6x√3 = 18√3
⇒ x = 3
घनों की भुजाएँ 9 cm, 12 cm और 15 cm होंगी।
∴ सही विकल्प 2 है।
Last updated on Jun 13, 2025
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