Two spheres of radius 9 units and 10 units are melted to form a sphere of radius 1 unit and another sphere. What is the value of the diameter of the other sphere (in units)?
Two spheres of radius 9 units and 10 units are melted to form a sphere of radius 1 unit and another sphere. What is the value of the diameter of the other sphere (in units)?
9 इकाई और 10 इकाई त्रिज्या वाले दो गोलों को पिघलाकर 1 इकाई त्रिज्या वाला एक गोला और एक दूसरा गोला बनाया जाता है। दूसरे गोले के व्यास का मान (इकाई में) ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
24
Volume is conserved (melting spheres):
$ \frac{4}{3}\pi (9^3 + 10^3) = \frac{4}{3}\pi (1^3 + R^3) $
Cancel common terms:
$9^3 + 10^3 = 1 + R^3$
Calculate:
$729 + 1000 = 1 + R^3$
$1729 = 1 + R^3$
$R^3 = 1728$
$R = 12$
Diameter = 2R = 24
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