1) A rectangular tank, 15 cm long and 20 cm wide, is filled with water to a depth of 12 cm. When a rock is put in, the water level rose to 15 cm. What is the volume of the rock?
change in volume = 15x20x3 cm^2
which must have been caused by the volume of the rock.
1444cm3 ans
Well, it seems like that rock did a great job displacing the water! To find the volume of the rock, we can use the concept of displacement. The water level rose by 3 cm when the rock was added. Since the rock doesn't have its own magical powers to expand, we can assume that the volume of water displaced by the rock is equal to the volume of the rock itself.
To calculate the volume of the rock, we can use the formula for the volume of a rectangular solid: length x width x height. In this case, since the rock's shape is not rectangular, we can approximate it by considering the rise in water level as the height. So, the volume of the rock would be 15 cm x 20 cm x 3 cm, which equals 900 cm³.
So, the volume of the rock is 900 cm³. It must be a pretty solid rock to displace that much water!
To find the volume of the rock, we need to calculate the change in the water level before and after the rock is added.
The initial water level is 12 cm, and after the rock is added, it rises to 15 cm.
The difference in the water level is: 15 cm - 12 cm = 3 cm.
Since the rock displaces the water, the volume of the rock is equal to the volume of water displaced.
The volume of water displaced can be calculated using the formula for the volume of a rectangular solid:
Volume = length x width x height
Given that the length is 15 cm, the width is 20 cm, and the height (change in water level) is 3 cm, we can substitute these values into the formula:
Volume = 15 cm x 20 cm x 3 cm = 900 cubic cm
Therefore, the volume of the rock is 900 cubic cm.
To find the volume of the rock, we need to calculate the change in water level when the rock is added.
Initially, the tank is filled with water to a depth of 12 cm. After the rock is added, the water level rises to 15 cm. This means the rock occupies a space of 3 cm (15 cm - 12 cm) in height.
The tank is rectangular, with dimensions of 15 cm (length) and 20 cm (width). Therefore, the base area of the tank is 15 cm * 20 cm = 300 cm².
To find the volume of the rock, we multiply the base area by the change in height:
Volume = base area * change in height
Volume = 300 cm² * 3 cm
Volume = 900 cm³
So, the volume of the rock is 900 cm³.