a hemisphere container is made with the following dimensions. the external diameter of the container is 12 cm. the internal diameter of the container is 6 cm. it is filled with water to the brim. what is the density of the empty container if the total mass of the container containing the water is 2156g? it is given that the volume of a sphere is 4/3pieR^3

To find the density of the empty container, we need to calculate its mass and volume.

First, let's find the mass of the empty container. We are given that the total mass of the container with water is 2156g. To find the mass of water, we need to subtract the mass of water from the total mass.

To determine the mass of water, we need to find the volume of water in the container and then multiply it by the density of water, which is approximately 1g/cm^3.

Now, let's calculate the volume of water in the container. The container is shaped like a hemisphere, so we need to find the volume of a hemisphere.

The volume of a hemisphere formula is V = (2/3) × π × r^3.

Given that the external diameter of the container is 12 cm, we can find the radius by dividing the diameter by 2. Thus, the radius (r) is 6 cm.

Now, we can calculate the volume of the hemisphere by substituting the values into the formula:
V = (2/3) × π × (6 cm)^3 = (2/3) × π × 216 cm^3 ≈ 452.39 cm^3.

Since the container is filled to the brim, the volume of water in the container is equal to the volume of the hemisphere, which is approximately 452.39 cm^3.

Now, let's find the mass of the water:
mass of water = density of water × volume of water = 1g/cm^3 × 452.39 cm^3 ≈ 452.39 g.

Now, we can find the mass of the empty container by subtracting the mass of the water from the total mass:
mass of empty container = total mass - mass of water = 2156g - 452.39g ≈ 1703.61 g.

Finally, we can find the density of the empty container:
density = mass/volume = 1703.61g/ (4/3 × π × (6 cm)^3) ≈ 1703.61g/ (4/3 × π × 216 cm^3) ≈ 1.36 g/cm^3.

Therefore, the density of the empty container is approximately 1.36 g/cm^3.