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Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

2. Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

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According to question, small spheres are melted and converted into a bigger sphere. Thus the sum of their volume is equal to the volume of the bigger sphere.

  The volume of 3 small spheres =  Volume of bigger sphere

Let us assume the radius of the bigger sphere is r.

\frac{4}{3}\pi \left ( r^3_1\ +\ r^3_2\ +\ r^3_3 \right )\ =\ \frac{4}{3}\pi r^3

r^3_1\ +\ r^3_2\ +\ r^3_3 \ =\ r^3

r^3\ =\ 6^3\ +\ 8^3\ +\ 10^3

r\ =\ 12\ cm

Hence the radius of the sphere obtained is 12 cm.

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