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

Question

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
___

Answer:
:
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 1stsphere + 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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