Aglass cylinder with aradius of 7cm has water up to aheight of 9cm. Ametal 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`
1.1
1.08m
To calculate the height by which the water rises in the cylinder, we can use the principle of displacement. The volume of water displaced by the cube when it is immersed in the cylinder is equal to the volume of the cube.
To find the height by which the water rises, we need to calculate the volume of the cube and compare it to the volume of the water displaced.
1. Calculate the volume of the cube:
The volume of a cube can be calculated by multiplying the length of one side by itself twice.
Volume of the cube = (Side length)^3 = 5.5 cm * 5.5 cm * 5.5 cm
2. Calculate the volume of the water displaced by the cube:
The volume of a cylinder can be calculated by multiplying the cross-sectional area of the cylinder by its height.
Cross-sectional area of the cylinder = π * (radius)^2
Volume of the water = Cross-sectional area of the cylinder * height of the water = π * (7 cm)^2 * 9 cm
3. Compare the volumes:
If the volume of the water displaced by the cube is equal to the volume of the cube, then the height by which the water rises in the cylinder is the same as the edge length of the cube. Otherwise, the height by which the water rises is less than the edge length of the cube.
If Volume of the water = Volume of the cube, then
π * (7 cm)^2 * 9 cm = 5.5 cm * 5.5 cm * 5.5 cm
Solve this equation to find the height by which the water rises.
Using the given values, you can calculate the height by which the water rises.