Final Answer:
The height of the water after 13 marbles are dropped into a container can be calculated using the principle of water displacement. The increase in water level will be equal to the total volume of the marbles is approximately 0.5447 cm.
Step-by-step explanation:
When marbles are dropped into a container filled with water, they displace an amount of water equal to their own volume. The volume of a sphere (marble) can be calculated using the formula V = 4/3 π r³, where r is the radius of the marble. Assuming each marble has a radius of 1 cm, the volume of one marble would be approximately 4.19 cm³. Therefore, for 13 marbles, the total volume would be 13 * 4.19 = 54.47 cm³.
Now, to find the increase in water level, we need to consider the dimensions of the container. Let’s assume the container is a rectangular prism with a base area of 100 cm^2 and an initial water height of 10 cm. Using the formula V = A * h, where V is the volume, A is the base area, and h is the height, we can rearrange it to solve for h: h = V / A. Plugging in our values, we get h = 54.47 cm³ / 100 cm² = 0.5447 cm.
Therefore, after dropping 13 marbles into the container, the water level will rise by approximately 0.5447 cm.
Complete the question:
What should be the height of the water after 13 marbles are dropped into a container, considering factors such as the size of the marbles, the volume of the container, and water displacement?