A glass cylinder with aradius of 7cm has water up to aheight of gcm. A metal cube of 5.5cm edge is immersed in it completely. Calculate the height by which the water rises in the cylinder.
When an object is immersed completely in water, the displaced volume of water is equal to the volume of the object.
The volume of cube is given by
V = s^3
where s = side length
Thus,
V = 5.5^3
V = 166.375 cm^3
The volume of cylinder is given by
V = π(r^2)(h)
where
π = 3.14
r = radius
h = height
We substitute the volume of cube to formula of volume of cylinder to solve for height:
166.375 = (3.14)(7^2)(h)
h = 166.375 / (3.14)(49)
h = ?
Units in cm. Hope this helps~ `u`
1.0813
To calculate the height by which the water rises in the cylinder, we can use the principle of displacement. According to Archimedes' principle, when an object is submerged in a fluid, it displaces an amount of fluid equal to its own volume.
First, let's find the volume of the metal cube using the formula:
Volume of a cube = edge length^3
The edge length of the cube is given as 5.5 cm, so the volume of the cube is:
Volume of the cube = 5.5 cm * 5.5 cm * 5.5 cm = 166.375 cm³
Now, let's calculate the volume of water displaced by the cube. Since the cube is completely immersed in water, the volume of water displaced will be equal to the volume of the cube.
Volume of water displaced = Volume of the cube = 166.375 cm³
Finally, let's calculate the height by which the water rises in the cylinder. The volume of water displaced is equal to the volume of the cylinder below the initial water level, up to the new water level.
The formula to calculate the volume of a cylinder is:
Volume of a cylinder = π * radius² * height
Since we are looking to find the height, we can rearrange the formula as follows:
Height = (Volume of water displaced) / (π * radius²)
Plugging in the values, we get:
Height = 166.375 cm³ / (π * 7 cm²)
Height ≈ 1.982 cm
Therefore, the water rises in the cylinder by approximately 1.982 cm.