A cylindrical column of plasticine has a radius of 3 cm and a height of 20 cm. Its weight is 8.25 N. Calculate the density of the plasticine.

The radius ($r$) is 3 cm, and the height ($h$) is 20 cm.

$$r = 3\, \text{cm} = 0.03\, \text{m}$$ $$h = 20\, \text{cm} = 0.20\, \text{m}$$

The formula for the volume of a cylinder is $V = \pi r^2 h$.

$$V = \pi (0.03\, \text{m})^2 (0.20\, \text{m})$$ $$V = \pi (0.0009\, \text{m}^2) (0.20\, \text{m})$$ $$V = 0.00018 \pi\, \text{m}^3$$ $$V \approx 0.00056548\, \text{m}^3$$

The weight ($W$) is 8.25 N. We use the formula $W = m \times g$, where $m$ is mass and $g$ is the acceleration due to gravity ($9.81\, \text{m/s}^2$).

$$m = \frac{W}{g}$$ $$m = \frac{8.25\, \text{N}}{9.81\, \text{m/s}^2}$$ $$m \approx 0.8409786\, \text{kg}$$

The formula for density ($\rho$) is $\rho = \frac{m}{V}$.

$$\rho = \frac{0.8409786\, \text{kg}}{0.00056548\, \text{m}^3}$$ $$\rho \approx 1487.25\, \text{kg/m}^3$$

Rounding to three significant figures:

$$\rho \approx 1490\, \text{kg/m}^3$$

The density of the plasticine is $\text{1490 kg/m}^3$.