​Three metallic spheres are of the radius 6 cm, 8 cm and 10 cm, respectively. If they are melted to form a single solid sphere, then the radius of the resulting sphere is

Correct option is C

​Given:

Radii of three metallic spheres:

$$r_1 = 6 \, \text{cm}, r_2 = 8 \, \text{cm}, r_3 = 10 \, \text{cm}$$​​

Formula Used:
Volume of a sphere$$V = \frac{4}{3} \pi r^3$$​​
Sum of the volumes = Volume of the resulting sphere.

Solution:  

​Let radius of resulting sphere = R

then,

Volume of resulting sphere = $$\frac{4}{3} \pi (6^3 + 8^3 + 10^3)$$​​

​$$\frac{4}{3} \pi R^3 = \frac{4}{3} \pi (1728)$$​​

​$$​​ R^3 = 1728$$​​

R = 12 cm​

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