6. In a toy factory, 200 wooden closed cylinders of diameter 35 mm and height 7 cm have to be painted. What is the total surface area, in \( \mathrm{cm}^{2} \), that needs to be painted? (Take \( \pi \) to be 3.142 . A tank in the shape of a cylinder of diameter

To find the total surface area that needs to be painted, we start by calculating the surface area of one cylinder. The total surface area (TSA) of a closed cylinder is given by the formula: \[ \text{TSA} = 2\pi r(h + r) \] Here, the radius \( r \) is half of the diameter, which is \( \frac{35 \text{ mm}}{2} = 17.5 \text{ mm} = 1.75 \text{ cm} \) and the height \( h \) is \( 7 \text{ cm} \). Plugging in the values: \[ \text{TSA} = 2 \times 3.142 \times 1.75(7 + 1.75) \] \[ = 2 \times 3.142 \times 1.75 \times 8.75 \] \[ \approx 2 \times 3.142 \times 1.75 \times 8.75 \approx 86.50 \, \text{cm}^2 \] Now for the total surface area for 200 cylinders: \[ \text{Total TSA} = 200 \times 86.50 \approx 17300 \, \text{cm}^2 \] So, the total surface area that needs to be painted is approximately \( 17300 \, \text{cm}^2 \). To put that into context, imagine how much paint you'd need: it's enough to cover a small room's wall! Just remember, the smoother the surface, the easier it will be to paint—ideal for those shiny wooden cylinders!