Question:
A metallic solid sphere of radius 6 cm is melted and recast into small spheres of radius 2 cm each. How many such small spheres are formed?
त्रिज्या 6 सेमी वाले एक ठोस धातु के गोले को पिघलाकर 2 सेमी त्रिज्या वाले छोटे गोले बनाए जाते हैं। ऐसे कितने छोटे गोले बनेंगे?
Options:
- 27
- 18
- 36
- 24
- 27
- 18
- 36
- 24
Correct Answer: a)
Explanation:
Number of spheres = \(\frac{\text{Volume of large sphere}}{\text{Volume of small sphere}} = \frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3} = \left(\frac{R}{r}\right)^3 = \left(\frac{6}{2}\right)^3 = 3^3 = \textbf{27}\) (Option a).
गोलों की संख्या = \((R / r)^3 = (6 / 2)^3 = 3^3 = \textbf{27}\) (विकल्प a)।