Two solid spheres with radii of 1 cm and 6 cm lengths are melted and a hollow sphere with an outer radius of 9 cm is made. Determine the inner radius of the new hollow sphere.
WBBSE
Class X
Mathematics
Sphere
04 Mark
2023
Volume of sphere = 4\over3πr³
Total volume of two sphere = 4\over3π(1³ + 6³)
Let internal radius of hollow sphere = r cm
Volume of the iron of this sphere = 4\over3π(9³ – r³)
According to the question,
4\over3π(1³ + 6³) = 4\over3π(9³ – r³)
or, (1³ + 6³) = (9³ – r³)
or, r³ = 9³ – 1³ – 6³ = 512
or, r³ = 8³
or, r = 8 cm
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