Final answer:
To find the minimum cost of painting the rod, calculate the surface area of the cylindrical rod and determine the number of tins of paint required. Divide the total surface area of the rod by the area covered by each tin of paint to find the number of tins. Round up to the nearest whole number and multiply by the cost per tin to find the minimum cost.
Step-by-step explanation:
To find the minimum cost of painting the rod, we need to calculate the surface area of the cylindrical rod and then determine the number of tins of paint required.
The surface area of a cylinder is given by the formula 2πrh + 2πr², where r is the radius and h is the height. In this case, the radius is half of the diameter, so it is 4.5m.
Plugging in the values, we get surface area = 2π(4.5m)(13m) + 2π(4.5m)² = 2π(58.5m²) + 2π(20.25m²) ≈ 408.41m².
Since each tin of paint covers 30m², we divide the total surface area of the rod by 30 to find the number of tins required = 408.41m² / 30m² ≈ 13.61 tins.
Since we can't have a fraction of a tin, we need to round up to the nearest whole number. So, we will need a minimum of 14 tins of paint.
The cost of 1 tin of paint is £5.30, so the minimum cost of painting the rod is 14 tins x £5.30 = £74.20.