(b) Two mathematically similar containers have heights of 30 cm and 75 cm . The larger container has a capacity of 5.5 litres. Calculate the capacity of the smaller container. Give your answer in millilitres.

To find the capacity of the smaller container, we can use the ratio of their heights. The larger container's height is 75 cm, and the smaller container's height is 30 cm. This gives us a height ratio of 30 cm / 75 cm = 2 / 5. Since the two containers are mathematically similar, the ratio of their volumes will be the cube of their height ratio. Therefore, (2/5) cubed equals 8/125. The larger container holds 5.5 litres, which is equivalent to 5500 millilitres. Now, we can set up the equation for the smaller container's volume: Smaller Container Volume = (8/125) * 5500 millilitres. Calculating that gives us: Smaller Container Volume = (8 * 5500) / 125 = 44000 / 125 = 352 millilitres. So, the capacity of the smaller container is 352 millilitres. Did you know that the concept of similar shapes dates back to ancient Greece? Mathematicians like Euclid defined the properties of similar figures, establishing a foundational understanding that still informs geometry today! The precision involved in calculating volumes assists not just in academic settings but also in practical fields like engineering and architecture, where knowing the capacity of containers can significantly affect design and functionality.