A floating cube is 10 cm on a side and has a density of 800 kg/m^3 . IT is floating in fresh water that has a density of 1000 kg/m^3. what percent of the cube is above the surface of the water?

Again, my professor says it is 20%, but how??

Maria/Andy/Ana/jessica

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the mass of the cube is density*volume=.8g/cm^3 * 1000cm^3=.8kg

the volume of the water displacing this (mass of water=8kg also)
volume=8kg/1000kg/m^3= (.8/1000)10^6 cm^3
= 800cm^3

So the volume above water is 200 cm^3 or 20 percent

To determine the percentage of the cube that is above the surface of the water, we can use the concept of buoyancy.

The buoyant force acting on an object is equal to the weight of the fluid displaced by the object. If the buoyant force is greater than or equal to the weight of the object, it will float; otherwise, it will sink.

Here's how you can calculate the percentage of the cube above the water surface:

Step 1: Calculate the weight of the cube:
The weight of an object can be found using the formula:
Weight = mass * gravity

Given that the density of the cube is 800 kg/m^3 and its volume is 10 cm^3 (since it is a cube with 10 cm on each side), we can calculate its mass:
Mass = density * volume

Convert the volume to m^3: 10 cm^3 = 10 * 10^-6 m^3
Mass = 800 kg/m^3 * 10 * 10^-6 m^3 = 8 * 10^-3 kg

Now, calculate the weight:
Weight = 8 * 10^-3 kg * 9.8 m/s^2 (acceleration due to gravity) = 0.0784 N

Step 2: Calculate the buoyant force:
The buoyant force can be found using the formula:
Buoyant force = weight of the fluid displaced

Since the cube is floating in fresh water, the weight of the fluid displaced is equal to the weight of the cube. Therefore, the buoyant force is also 0.0784 N.

Step 3: Determine the part of the cube above the water surface:
The buoyant force acting on the cube is equal to the weight of the fluid displaced by the submerged part of the cube. Since the cube is floating, the buoyant force is greater than or equal to the weight of the cube.

Hence, since the buoyant force is equal to the weight of the cube, the entire cube is submerged in the water, and none of it is above the water surface.

Therefore, the professor's answer of 20% is incorrect. In this case, none of the cube is above the surface of the water.