Dr Seroto the head of Maths, Science and Technology has to produce rectangular display doarcs when organising a science fair. The external dimensions of each board are 52 inches by 40 inches. The front surfaces of the boards must be spray - painted with one layer of non- reflective white paint. NOTE: \( 1 \mathrm{~m} \mathrm{\ell} \) of the paint covers a surface area of \( 50 \mathrm{~cm}^{2} \) 1 inch \( =25 \mathrm{~mm} \) Use information above to answer the questions \( \begin{array}{l}3.1 \text { Determine, showing ALL calculations, whether } 8 \text { litres of the paint would be enough to } \\ \text { spray paint } 30 \text { display boards. The following formula may be used: } \\ \text { Area }=\text { length } \times \text { width }\end{array} \)

To determine if 8 liters of paint is sufficient for 30 display boards, we first need to calculate the total area that needs to be painted. Each board's dimensions are 52 inches by 40 inches. First, we find the area in square inches: Area of one board = 52 inches × 40 inches = 2080 square inches. Now, calculating for 30 boards: Total area = 30 boards × 2080 square inches = 62400 square inches. Next, we convert square inches to square centimeters, since 1 inch = 2.54 cm: Total area in cm² = 62400 square inches × (2.54 cm/inch)² = 403200 cm². Now, to find out how much paint is needed, we divide the total area by the cover area of the paint: Paint required = Total area / Coverage per liter = 403200 cm² / 50 cm²/l = 8064 liters. Since 8 liters is far less than the 8064 liters required, we conclude that 8 liters of paint is not enough for 30 boards. To be practical, if you're ever calculating paint needs, always check both the area and coverage ratios—you wouldn’t want to run out mid-spray! The old adage “measure twice, paint once” certainly rings true here. Did you know that the average person spends more time choosing the right paint than actually applying it? It's true! Choosing the right paint can enhance a space not just visually but also in terms of functionality and durability. If you're curious about paint types and their unique properties, diving into the world of finish types—like matte, eggshell, or satin—might just inspire the artist in you!