Question : A solid metallic sphere of radius x cm is melted and then drawn into 126 cones each of radius 3.5 cm and height 3 cm. There is no wastage of material in this process. What is the value of $x$?
Option 1: 10.5
Option 2: 3.5
Option 3: 7
Option 4: 21
Correct Answer: 10.5
Solution :
The volume of the sphere = $\frac {4}{3}\pi r^3$,
Volume of a cone = $\frac{1}{3}\pi r^2h$, where $r$ = radius, $h$ = height
According to the question,
$\frac {4}{3}\pi r^3= 126 × \frac{1}{3}\pi r^2h$
⇒ $x^{3} = \frac{126}{4} × 3.5 × 3.5 × 3$
⇒ $x^{3} = 3 × 3 × 3.5 × 3.5 × 3.5 × 3$
$\therefore x = 3 × 3.5 = 10.5$
Hence, the correct answer is 10.5.
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