Question : A metallic solid sphere has a radius of 35 cm. If it is melted to form small spheres of radius 5 cm, then how many small spheres will be obtained?
Option 1: 343
Option 2: 289
Option 3: 429
Option 4: 369
Correct Answer: 343
Solution :
For the large sphere with a radius of 35 cm,
⇒ $V_1 = \frac{4}{3}π(35)^3$
Now, for the small spheres with a radius of 5 cm,
⇒ $V_2 = \frac{4}{3}π(5)^3$
So, the number of small spheres = $\frac{V_1}{V_2}$
= $\frac{\frac{4}{3}π(35)^3}{\frac{4}{3}π(5)^3}$
= $\frac{(35)^3}{(5)^3}$
= $7^3$
= $343$
Hence, the correct answer is 343.
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