Final answer:
The amount of paint required to cover the curved surface area of a cylindrical can with a surface area of 900 square meters and 30 cm tall depends on the paint's coverage rate. Solve for the radius using the formula 2πrh and use the coverage rate to calculate the necessary paint quantity.
Step-by-step explanation:
The question asks about calculating the amount of paint needed to cover the curved surface area of a cylindrical can. The can is said to have a curved surface area of 900 square meters and is 30 cm tall. To find out how much paint is required, one needs to consider that the curved surface area of a cylinder is given by the formula 2πrh, where r is the radius and h is the height of the cylinder.
Given that the height h is 30 cm, or 0.3 m, we can rearrange the formula to find the radius r: 900 m² = 2πr(0.3 m). Solving this equation for r gives us the radius. Knowing the radius and the height, we would typically use the volume formula V = πr²h, but since we're only interested in painting the curved surface and the can has no lid, the volume is not directly relevant here.
Instead, the amount of paint will depend on the paint's coverage rate in square meters per liter, which is often specified by the manufacturer. Without this information, we cannot provide an exact quantity of paint needed. Nonetheless, once the radius is found and the manufacturer's coverage rate is known, one could easily calculate the amount of paint required for the project.