A glass bead is made by turning the region between the curves y = √x and y = x/2 about the x-axis…

Step 1. Meeting points. $\sqrt{x} = \dfrac{x}{2}$ gives $x = \dfrac{x^2}{4}$, so $x = 0$ or $x = 4$.

Step 2. Washers. The outer radius is $R = \sqrt{x}$ and the inner radius is $r = \dfrac{x}{2}$. So $V = \pi\displaystyle\int_0^4 \left(x - \dfrac{x^2}{4}\right)dx$.

Step 3. Evaluate. $\left[\dfrac{x^2}{2} - \dfrac{x^3}{12}\right]_0^4 = 8 - \dfrac{16}{3} = \dfrac{8}{3}$. So $V = \dfrac{8\pi}{3} \approx 8.38$ cm$^3$.

Step 4. Mass. $2.5\ \text{g/cm}^3 \times 8.38\ \text{cm}^3 \approx 20.94$ g.