A hollow metallic sphere has outer radius 10 cm and is melted to make 50 smaller solid spheres of radius 2 cm.
A hollow metallic sphere has outer radius 10 cm and is melted to make 50 smaller solid spheres of radius 2 cm. What is the inner radius of the original sphere?
एक खोखले धातु के गोले की बाहरी त्रिज्या 10 सेमी हैं। और इसे पिघलाकर 2 सेमी त्रिज्या वाले 50 छोटे ठोस गोले बनाए जाते हैं। मूल गोले की आंतरिक त्रिज्या क्या हैं?
Detailed Solution & Logic
Correct Answer:
8.43 cm
Let the inner radius of the hollow sphere be $r$ cm.
Volume of metal in the hollow sphere
$=\dfrac{4}{3}\pi(10^3-r^3)$
Volume of $50$ solid spheres
$=50\times\dfrac{4}{3}\pi(2^3)$
Equating the volumes,
$\dfrac{4}{3}\pi(1000-r^3)=50\times\dfrac{4}{3}\pi(8)$
$1000-r^3=400$
$r^3=600$
$r=\sqrt[3]{600}\approx 8.43\text{ cm}$
Answer
$\sqrt[3]{600}\text{ cm}\approx 8.43\text{ cm}$
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