Question
Download Solution PDFजर 10 सेमी त्रिज्येचा एक घन गोल समान त्रिज्येच्या 8 गोलाकार घन गोलांमध्ये वितळवला, तर अशा प्रत्येक गोळ्याचे पृष्ठफळ किती असेल? [π = \(\frac{{22}}{7}\) वापरा].
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
R = 10 सेमी
वापरलेले सूत्र:
घनफळ = 4/3 x 22/7 x R x R x R
एकुण पृष्ठफळ (TSA) (गोल) = 4 x 22/7 x r x r
उकल:
मोठ्या घन गोलाचे घनफळ = 4/3 x 22/7 x 103
आपल्याकडे समान त्रिज्येचे एकुण 8 लहान गोल आहेत.
लहान गोलाचे घनफळ = 4/3 x 22/7 x r3
मोठ्या गोलाचे घनफळ = 8 × लहान गोलाचे घनफळ
4/3 x 22/7 x 103 = 8 × 4/3 x 22/7 x r3
⇒ r3 = 1000/8
⇒ r = 5 सेमी
एकुण पृष्ठफळ (TSA) (गोल) = 4 x 22/7 x 52
= 88/7 x 25
= 314.285714 = 314 \(2\over7\) सेमी2
म्हणून, पर्याय 2 योग्य आहे.
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