Problem Statement
A metallic solid cone of height $24\text{ cm}$ and base radius $6\text{ cm}$ is melted and reshaped into the shape of a solid sphere. Find the radius of the sphere.
Verified Solution & Marking Scheme
Equate Volumes of Cone and Sphere
$$\text{Volume of cone} = \frac{1}{3}\pi r_{\text{cone}}^2 h = \frac{1}{3}\pi (6^2)(24) = \frac{1}{3}\pi (36)(24) = 288\pi\text{ cm}^3$$
$$\text{Volume of sphere} = \frac{4}{3}\pi R^3$$
$$\frac{4}{3}\pi R^3 = 288\pi$$
Solve for Sphere Radius R
$$\frac{4}{3} R^3 = 288 \implies R^3 = 288 \times \frac{3}{4} = 72 \times 3 = 216$$
$$R = \sqrt[3]{216} = 6\text{ cm}$$