To calculate the volume of the cylindrical tin of paint, we can use the formula for the volume of a cylinder:

$V = \pi r^2 h$

Where:

• $r$ is the radius of the base of the cylinder,
• $h$ is the height of the cylinder.

From the diagram:

• Diameter of the base = $9 \, \text{cm}$, so the radius $r = \frac{9}{2} = 4.5 \, \text{cm}$,
• Height $h = 20 \, \text{cm}$.

Now substitute these values into the formula:

$V = \pi (4.5)^2 (20)$

$V = \pi (20.25) (20)$

$V = \pi (405)$

$V = 405\pi \, \text{cm}^3$

Thus, the volume of the cylindrical tin of paint is:

$\boxed{405\pi \, \text{cm}^3}$

Let me know if you need a step-by-step breakdown or further clarification!

Here are 5 related questions to explore:

1. How do you convert the volume in terms of $\pi$ to an approximate numerical value?
2. What happens to the volume if the height of the cylinder doubles?
3. Can you calculate the surface area of this cylindrical tin?
4. How does changing the radius affect the volume, assuming the height remains constant?
5. If the tin was filled with paint, how would you calculate the weight of the paint based on its density?

Tip: Always double-check your measurements when substituting into formulas to avoid errors!