A plastic cube having a side of length 10cm floats on fresh water. If the volume of the cube that is submerged into water is 40 percent of its total volume ,what is the density of the cube?
Let's start by finding the volume of the cube. Since the cube has a side length of 10cm, its volume is:
V = s^3 = 10^3 = 1000 cm^3
Next, we can find the volume of the cube that is submerged in water. We know that this volume is 40% of the total volume, so we can write:
V_submerged = 0.4V = 0.4(1000) = 400 cm^3
To find the density of the cube, we need to know its mass. We can use the fact that the cube is floating to find its mass. When an object is floating, the buoyant force (which is equal to the weight of the water displaced by the object) is equal to the weight of the object. Since the cube is not sinking or floating to the top, we know that its weight (which is equal to its mass times gravity) is equal to the buoyant force. In other words:
weight = buoyant force
m*g = ρ_water*V_submerged*g
where m is the mass of the cube, g is the acceleration due to gravity, ρ_water is the density of fresh water, and V_submerged is the volume of water displaced by the cube (which we found earlier).
Simplifying this equation, we can solve for the mass of the cube:
m = ρ_water*V_submerged
Plugging in the values we know, we get:
m = 1000 kg/m^3 * 0.4 * 10^-3 m^3 = 0.4 kg
Finally, we can find the density of the cube by dividing its mass by its volume:
ρ = m/V = 0.4 kg / 0.001 m^3 = 400 kg/m^3
Therefore, the density of the cube is 400 kg/m^3.
Ah, the floating plastic cube in fresh water puzzle. Let's dive right into it, shall we?
To find the density of the cube, we need to know the weight of the water it displaces. Since it's floating, the weight of the cube is equal to the weight of the water it displaces.
Now, if 40 percent of the cube's volume is submerged, that means the remaining 60 percent is above water, possibly chilling with some rubber duckies.
Since a cube has equal dimensions, we can say that 60 percent of its volume is above water, and the remaining 40 percent is below.
Now, imagine that 40 percent submerged portion as a mini-submarine, exploring the depths of H2O.
Since we know the submerged volume, which is 40 percent of the total volume, we can calculate the weight of the water displaced.
But how do we do that, you ask? Well, it's a bit "densified," I must say.
The density of fresh water is roughly 1 gram/cm³ or 1000 kg/m³. So to find the density of the cube, we need to find the weight of the water it displaces and divide that by the volume of the submerged portion.
Since density equals mass divided by volume, and we already know the volume of the submerged portion, all we need is the mass of water displaced.
With these equations swimming around, we can now calculate the density of the cube. Dive in and do the math, my friend.
To find the density of the cube, we'll need to use the formula:
Density = Mass / Volume
We know that the volume submerged in water is 40% of the total volume of the cube. Given that the side length of the cube is 10cm, we can find the volume of the cube submerged as follows:
Volume submerged = (40/100) * (10cm)^3
= (40/100) * 1000 cm^3
= 400 cm^3
Since the cube is made of plastic, we can assume its density is constant. Therefore, the density of the submerged portion is the same as the density of the entire cube.
Now, let's calculate the total volume of the cube:
Total volume = (10cm)^3
= 1000 cm^3
We know that the volume submerged is 400 cm^3. Therefore, the volume not submerged (above water) is:
Volume above water = Total volume - Volume submerged
= 1000 cm^3 - 400 cm^3
= 600 cm^3
Since the density of the cube is constant, we can use the formula to find the mass:
Density = Mass / Volume
Rearranging the formula, we have:
Mass = Density * Volume
To find the mass of the cube, we'll use the volume above water:
Mass = Density * Volume above water
= Density * 600 cm^3
Now, substituting the given volume submerged:
Mass = Density * (600 cm^3 + 400 cm^3)
= Density * 1000 cm^3
Now we have the mass in terms of the density and volume.
Substituting in the formula for density:
Density = Mass / Volume
= (Density * 1000 cm^3) / 1000 cm^3
= Density
Hence, the density of the plastic cube is equal to the density of water, which is approximately 1 g/cm^3.
To find the density of the cube, we need to know two things: the mass of the cube and its volume.
First, let's find the volume of the cube. Given that 40 percent of its total volume is submerged, we know that 60 percent is above the water surface. This means that the submerged volume is 40 percent of the total volume and the remaining 60 percent is above the water.
Using this information, we can set up the following equation:
Volume_submerged = 40% * Total_volume
We can rearrange the equation to solve for the total volume:
Total_volume = Volume_submerged / 40%
Now, let's substitute the known values:
Total_volume = Volume_submerged / 0.40
Next, we need to calculate the volume of the cube using the formula for the volume of a cube:
Volume = side_length^3
Substituting the side length as 10cm:
Volume = 10cm * 10cm * 10cm
Volume = 1000 cm^3
Now, we can substitute the value of Total_volume into the equation and calculate the submerged volume:
1000 cm^3 = Volume_submerged / 0.40
To find the volume submerged, we multiply the total volume by 40% (or 0.40):
Volume_submerged = 1000 cm^3 * 0.40
Volume_submerged = 400 cm^3
Now that we have the volume submerged, we need to find the mass of the cube. To do this, we can use the equation:
Density = Mass / Volume
Given that the cube is floating in fresh water, the density of the cube is equal to the density of water, which is approximately 1000 kg/m^3.
Now, we can calculate the mass of the cube using the density and the submerged volume:
Density_cube = Density_water = Mass_cube / Volume_submerged
Rearranging the equation, we can solve for Mass_cube:
Mass_cube = Density_water * Volume_submerged
Substituting the values:
Mass_cube = 1000 kg/m^3 * 400 cm^3
To proceed with the calculations, we need to convert the volume and density units to the same unit. Since mass is usually measured in grams, let's convert the density to g/cm^3:
Density = 1000 kg/m^3 * (1 g/1000 kg) * (1 m^3/1000000 cm^3)
Density = 0.001 g/cm^3
Now, we can calculate the mass of the cube:
Mass_cube = 0.001 g/cm^3 * 400 cm^3
Mass_cube = 0.4 g
Finally, we can substitute the values of Mass_cube and Volume_submerged
Density_cube = Mass_cube / Volume_submerged
Density_cube = 0.4 g / 400 cm^3
Density_cube = 0.001 g/cm^3
Therefore, the density of the plastic cube is 0.001 g/cm^3.