A solid metallic sphere of radius 12 cm is melted to form three smaller spheres. If the radii of two spheres are 6 cm and 8 cm, find the radius of the third sphere.

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1. Volume of the large sphere: $V=(4/3)\pi(12)^3=2304\pi$.
2. Volumes of the two small spheres: $V_1=(4/3)\pi(6)^3=288\pi$, $V_2=(4/3)\pi(8)^3=\frac{2048}{3}\pi$.
3. Remaining volume = $2304\pi-(288\pi+\frac{2048}{3}\pi)=\frac{4000}{3}\pi$.
4. For the third sphere $(4/3)\pi r^3=\frac{4000}{3}\pi$, so $r^3=1000$ and $r=10$ cm.
FINAL_ANSWER: a

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