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 first calculate the volume of the empty hemisphere and then use the given mass of the container to calculate its density.
Let's break down the problem step by step:
Step 1: Calculate the radius of the container.
The external diameter of the container is 12 cm, so the internal radius would be half of that, which is 6 cm.
Step 2: Calculate the volume of the empty hemisphere.
The volume of a sphere is given by the formula V = (4/3) * π * r^3, where r is the radius. However, in this case, we only need to find the volume of a hemisphere since the container is cut in half.
Substituting the radius into the formula, we get:
V = (4/3) * π * (6 cm)^3
V = (4/3) * π * 216 cm^3
Step 3: Calculate the density of the empty container.
Density is defined as mass divided by volume. In this case, we have the mass of the container.
Density = Mass / Volume
Density = 2156 g / (4/3 * π * 216 cm^3)
Step 4: Solve for density.
Now we can calculate the density of the empty container by substituting the values into the equation:
Density = 2156 g / (4/3 * π * 216 cm^3)
Calculating the value on the right side:
Density = 2156 g / (0.5236 * 216 cm^3)
Density = 2156 g / 113.0976 cm^3
Density ≈ 19.06 g/cm^3
Therefore, the density of the empty container is approximately 19.06 g/cm^3.