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By melting a solid lead sphere of diameter 12 cm, three small spheres are made whose diameters are in the ratio 3 : 4 : 5. The radius (in cm) of the smallest sphere is
By melting a solid lead sphere of diameter 12 cm, three small spheres are made whose diameters are in the ratio 3 : 4 : 5. The radius (in cm) of the smallest sphere is
1). 3
2). 6
3). 1.5
4). 4
1 answers
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Volume of sphere = 4/3 × πr3
Radius of solid lead sphere = 12/2 = 6cm
Volume of big solid lead sphere =
= $(\frac{4}{3}{\rm{}} \times {\rm{}}\pi {\rm{}} \times {\rm{}}{6^3})$
= 288π cubic cm
Given,
Radius of three small spheres are 3A, 4A, 5A respectively.
Given,
⇒ 288π = (4/3) × π × [(3A)3 + (4A)3 + (5A)3]
⇒ 216 = 216A3
⇒ A = 1
Radius of circle = 3 cm, 4 cm, 5 cm
∴ Radius of smallest sphere is 3 cm.Other Questions
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