Metallic spheres of radii 6cm, 8cm and 10cm, respectively are melted to form

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Metallic spheres of radii 6cm, 8cm and 10cm, respectively are melted to form a single solid sphere. The radius of the resulting sphere(in cm) is

___

Options:

Answer: Option A
:

Radius of first Sphere = $r_{1} = 6 c m$

Radius of second Sphere = $r_{2} = 8 c m$

Radius of third Sphere = $r_{3} = 10 c m$
Let radius of resulting sphere = r cm
According to given condition, we have
Volume of 1st sphere + Volume of 2nd sphere + Volume of 3rd sphere = Volume of resulting sphere
$\Rightarrow \frac{4}{3} . π . (r_{1})^{3} + \frac{4}{3} . π . (r_{2})^{3} + \frac{4}{3} . π . (r_{3})^{3} = \frac{4}{3} . π . r^{3}$

$\Rightarrow \frac{4}{3} ((r_{1})^{3} + (r_{2})^{3} + (r_{3})^{3}) = \frac{4}{3} . r^{3}$

$\Rightarrow$ $(6^{3} + 8^{3} + (10)^{3}) = r^{3}$

$\Rightarrow$ ( 216 + 512 + 1000 ) = $r^{3}$

$\Rightarrow$ $r^{3}$ = 1728

$\Rightarrow$ r = 12 cm

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