Question

A hollow spherical body of inner and outer radii $6cm$ and $8cm$ respectively floats half-submerged in water. Find the density of the material of the sphere.

Answer 1

Volume of water displaced = $\frac{4}{3}\frac{\pi {\left(8cm\right)}^3}{2}$

= $\frac{4}{3}\pi \times \frac{8^3}{2}cc$

Mass of body = $\frac{4}{3}\frac{\pi 8^3}{2}cc\times 1gm/cc$

= $\frac{2}{3}\pi 8^{3}gm$

and volume of material in body = $\frac{4}{3}\pi (8^3-6^3)$

= $\frac{4}{3}\pi 296cc$

So density = $\frac{mass}{volume}=\frac{\frac{2}{3}\pi 8^3}{\frac{4}{3}\pi \times 296}=0.864\frac{gm}{cc}$