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CBSE Class 10 Answered

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Asked by | 27 Feb, 2013, 11:05: PM
Expert Answer
Let the radius of 2 spheres be r1 and r2 and weights be W1 and W2 respectively such that W1 = 1kg, and W2 = 7kg. Also, r1 = 3cm.
 
Weight of the sphere = (density) * Volume
Since the density of the 2 sphere will be same as they are made from the same metal, so
W1/V1 = W2/V2 (density = Weight/volume)
Also, since the volume of a sphere = 4/3 (pi) r3
Hence, W1/4/3 (pi) r13 = W2/4/3 (pi) r23
1/(3)3 = 7/r23
 
i.e. r23 = 7*27 = 189
 
Now, volume of the bigger sphere = V1 + V2 (since the bigger sphere is made by melting the 2 smaller spheres)
 
4/3 (pi) R3 = 4/3 (pi) r13 + 4/3 (pi) r23
i.e. R3 = (3)3 + 189
R = 6 cm
Hence, diameter of the bigger sphere = 2* 6 cm = 12 cm
Answered by | 28 Feb, 2013, 04:54: AM
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