Problem Statement
Metallic spheres of radii $6\text{ cm}, 8\text{ cm}$ and $10\text{ cm}$ respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
Verified Solution & Marking Scheme
Equate Volumes
Volume of resulting sphere equals sum of volumes of three smaller spheres:
$$\frac{4}{3}\pi R^3 = \frac{4}{3}\pi r_1^3 + \frac{4}{3}\pi r_2^3 + \frac{4}{3}\pi r_3^3$$
Calculate Cubes
$$R^3 = 6^3 + 8^3 + 10^3 = 216 + 512 + 1000 = 1728$$
Find Cube Root
$$R = \sqrt[3]{1728} = 12\text{ cm}$$