A rectangular container has a 10 cm square base and contains water to a depth of 12 cm. when a stone of a mass of 600 g is gently lowered into the water , the level rises to 14 cm.calculate the volume of water displaced
the volume occupied by water and/or stone has risen from
10^2 * 12 to 10^2 * 14 = 200cm^3
so, ...
next question is no doubt to find the density of the stone.
Density of the stone
To calculate the volume of water displaced by the stone, you can use the principle of displacement.
1. Start with the initial volume of water in the container. The base area of the container is 10 cm by 10 cm, so the initial volume is 10 cm x 10 cm x 12 cm = 1200 cm^3.
2. After the stone is added, the water level rises to 14 cm. So, the new volume of water in the container is 10 cm x 10 cm x 14 cm = 1400 cm^3.
3. The difference between the initial volume and the final volume represents the volume of water displaced by the stone. Therefore, the volume of water displaced is 1400 cm^3 - 1200 cm^3 = 200 cm^3.
So, the volume of water displaced by the stone is 200 cm^3.
To calculate the volume of water displaced, we need to find the difference in volume before and after the stone is added.
First, we need to find the initial volume of water in the container, which is the volume up to a depth of 12 cm.
The formula for the volume of a rectangular container is given by:
Volume = length * width * height
In this case, the length and width are both 10 cm, and the height (depth) is 12 cm.
So, the initial volume of water in the container is:
Volume_initial = 10 cm * 10 cm * 12 cm = 1200 cm³
Next, we need to find the volume of the stone. Since the stone is fully submerged, the volume of water displaced by the stone is equal to the volume of the stone.
Given that the mass of the stone is 600 g, we can use the density formula to find its volume:
Density = mass / volume
Rearranging the formula, we get:
Volume = mass / density
We need to convert the mass from grams to kilograms since the density is usually given in kg/m³.
Mass = 600 g = 600/1000 kg = 0.6 kg (1 kg = 1000 g)
Now, we assume the density of the stone to be the same as the density of water, which is approximately 1000 kg/m³.
Thus, the volume of the stone (and therefore the volume of water displaced) is:
Volume_displaced = 0.6 kg / 1000 kg/m³ = 0.0006 m³ = 600 cm³
Finally, the volume of water displaced is the difference between the volume after the stone is added and the initial volume:
Volume_displaced = Volume_final - Volume_initial
Given that the final height is 14 cm, we can calculate the final volume:
Volume_final = 10 cm * 10 cm * 14 cm = 1400 cm³
Therefore, the volume of water displaced is:
Volume_displaced = 1400 cm³ - 1200 cm³ = 200 cm³
So, the volume of water displaced is 200 cm³ or 0.2 L.