3. Arectangular tank mousuring 40 cm by 30 cm by 20 cm is \( \frac{1}{4} \) filled with, water. How many more litres of water are needed so that \( \frac{4}{5} \) of the tank is filled with water?

To find out how much more water is needed, first, calculate the volume of the tank. The volume of the tank is given by multiplying its dimensions: \(40 \, \text{cm} \times 30 \, \text{cm} \times 20 \, \text{cm} = 24000 \, \text{cm}^3\). To convert this to liters, remember that 1000 cm\(^3\) equals 1 liter, so the total volume of the tank is 24 liters. Currently, the tank is \( \frac{1}{4} \) filled, which means it contains \( \frac{1}{4} \times 24 = 6 \) liters of water. We want to fill the tank to \( \frac{4}{5} \) of its total volume: \( \frac{4}{5} \times 24 = 19.2 \) liters. Now, subtract the current amount of water from the desired amount: \( 19.2 \, \text{liters} - 6 \, \text{liters} = 13.2 \, \text{liters} \). Thus, 13.2 more liters of water are needed to fill the tank to \( \frac{4}{5} \). To make sure your calculations stay error-free, keep an eye on unit conversions. It’s easy to mix up volume measurements, especially when switching from cubic centimeters to liters. Double-check every step, and always write down the formulae or conversions you're using, just to keep your thinking clear!