यदि किसी गोले की त्रिज्या आधी कर दी जाए, तो नया आयतन मूल आयतन का ________ हो जाएगा।

This question was previously asked in
RRB Group D 16 Sept 2022 Shift 3 Official Paper
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  1. \(\frac{1}{4}\) गुना 
  2. 8 गुना 
  3. 4 गुना 
  4. \(\frac{1}{8}\) गुना 

Answer (Detailed Solution Below)

Option 4 : \(\frac{1}{8}\) गुना 
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Detailed Solution

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प्रयुक्त सूत्र:

गोले का आयतन = \(\frac{4}{3}πr³\)

गणना:

त्रिज्या आधी हो जाती है अर्थात् नई त्रिज्या = \(\frac{r}{2}\)

अब, नया आयतन 

\((\frac{4}{3})π(\frac{r}{2})³\)

\((\frac{4}{3})(πr³)(\frac{1}{8})\)

\(\frac{आयतन}{8}\)

अतः, आयतन \(\frac{1}{8}\) गुना हो जाएगा।

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