A cylinder with internal diameter of

5cm and 15 cm high is filled up with an unknown substance.
The mass of the cylinder is 4.6 kg which is 300% of the unknown substance
mass. Determine the density and the specific gravity of the unknown substance.

density=mass/volume=

mass stuff= 1/4 4.6 kg if I read your statment correctly. I am uncertain if when it is said the "mass of the cylinder" that means the cylinder with the stuff, or the cylinder itself. I took it as the cylinder with the stuff.

densiy= (.25*4.6)kg/(PI (2.5^2*15) kg/cm^3

To solve this problem, we can follow the following steps:

Step 1: Find the mass of the unknown substance.
Since the mass of the cylinder is 4.6 kg and it is 300% of the unknown substance's mass, we can calculate the unknown substance's mass by dividing the mass of the cylinder by 300% (or 3):
Unknown substance mass = 4.6 kg / 3 = 1.53 kg

Step 2: Calculate the volume of the cylinder.
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
Given that the internal diameter of the cylinder is 5 cm, the radius (r) is half of the diameter, so r = 5 cm / 2 = 2.5 cm = 0.025 m.
The height (h) is given as 15 cm = 0.15 m.
Substituting the values into the formula:
V = π(0.025 m)^2(0.15 m)
V ≈ 0.00589 m^3

Step 3: Calculate the density of the unknown substance.
Density is defined as mass divided by volume:
Density (ρ) = Mass / Volume
ρ = 1.53 kg / 0.00589 m^3
ρ ≈ 260.38 kg/m^3

Step 4: Calculate the specific gravity.
Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water).
To find the specific gravity, we need to compare the density of the unknown substance to the density of water.
The density of water at standard conditions is approximately 1000 kg/m^3.
Specific gravity = Density of unknown substance / Density of water
Specific gravity ≈ 260.38 kg/m^3 / 1000 kg/m^3
Specific gravity ≈ 0.260

Therefore, the density of the unknown substance is approximately 260.38 kg/m^3, and its specific gravity is approximately 0.260.