A solid cube of side 8cm is dropped into a cylindrical tank of radius 7cm.calculate the rise in the water level if the original depth of water was 9cm
The volume of the cube is V1 = (8 cm)^3 = 512 cm^3.
The volume of water displaced by the cube when it is completely submerged is equal to the volume of the cube, which is 512 cm^3.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
If the original depth of water was 9cm, the initial height of the water in the cylinder is h1 = 9cm.
After the cube is dropped in, the volume of water in the cylinder increases by 512 cm^3. Therefore:
πr^2h2 - πr^2h1 = 512
πr^2(h2 - h1) = 512
h2 - h1 = 512 / (πr^2)
h2 - 9 = 512 / (π(7)^2)
h2 - 9 ≈ 1.45 cm
Therefore, the water level rises by approximately 1.45 cm.
To calculate the rise in the water level, we need to find the volume of the cube and the volume of the water displaced by it.
The volume of the cube can be found using the formula: volume = side^3
Given that the side of the cube is 8 cm, the volume of the cube is:
Volume of the cube = 8^3 = 512 cm^3
The volume of the water displaced by the cube will be equal to the volume of the cube, since the cube is completely submerged in water.
Now, we need to find the rise in the water level, which is equal to the volume of the water displaced divided by the base area of the cylindrical tank.
The volume of the water displaced is 512 cm^3, and the base area of the cylindrical tank can be found using the formula: base area = pi * radius^2
Given that the radius of the cylindrical tank is 7 cm, the base area of the cylindrical tank is:
Base area of the cylindrical tank = pi * 7^2 = 49pi cm^2 (approximately 153.94 cm^2)
Now, we can calculate the rise in water level:
Rise in water level = Volume of water displaced / Base area of cylindrical tank
= 512 cm^3 / 153.94 cm^2
= 3.33 cm (approximately, rounded to two decimal places)
Therefore, the rise in the water level is approximately 3.33 cm.