1. **Problem statement:** A student is determining the density of sand using a beaker. The beaker has a mark at 250 cm^3, and the student estimates the total volume of water the beaker can hold as 270 cm^3. The circumference of the beaker is measured as 21.3 cm. 2. **Part (a): Estimate the volume of water $V_w$ the beaker holds when filled to the top.** Given: $V_w = 270$ cm$^3$ (already provided as an estimate). 3. **Part (b): Determine the radius $r$ of the beaker from the circumference $c$.** The formula relating circumference and radius is: $$c = 2\pi r$$ 4. **Calculate the radius $r$: ** $$r = \frac{c}{2\pi}$$ Substitute $c = 21.3$ cm: $$r = \frac{21.3}{2\pi}$$ 5. **Simplify the expression:** $$r = \frac{21.3}{2 \times 3.1416} = \frac{21.3}{6.2832}$$ 6. **Calculate the numerical value:** $$r \approx 3.39 \text{ cm}$$ --- **Final answers:** - Volume of water the beaker holds when filled to the top: $V_w = 270$ cm$^3$ - Radius of the beaker: $r \approx 3.39$ cm