If the diameter of the black marble is 3.0 cm, and by using the formula for volume, what is a good approximation of its volume? Record to the ones place.
___cm3
Determine the initial volume of water in the graduated cylinder. If you added the black marble to the graduated cylinder and it sinks, what final volume should the water level indicate? Record to the ones place.
___mL
To calculate the volume of the black marble, we need to use the formula for the volume of a sphere:
Volume = (4/3) * π * radius^3
The diameter of the black marble is given as 3.0 cm, so the radius would be half of that, which is 1.5 cm.
Plugging the values into the formula, we get:
Volume = (4/3) * π * (1.5 cm)^3
≈ 14.1 cm^3
So, a good approximation of the volume of the black marble is 14 cm^3.
The initial volume of water in the graduated cylinder is not provided, so we cannot determine its exact value. However, if we assume the cylinder was initially empty, then adding the black marble (which sinks) to it would displace an equal volume of water.
Since we determined the volume of the black marble earlier to be approximately 14 cm^3, the water level should indicate a final volume of approximately 14 mL.
To find the volume of the black marble, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
Where V is the volume and r is the radius. The diameter of the marble is given as 3.0 cm, so the radius is half of that, which is 1.5 cm.
1. Calculating the volume:
V = (4/3) * π * (1.5)^3
V ≈ 1.77 cm^3 (rounded to the ones place)
Therefore, a good approximation of the volume of the black marble is 2 cm^3.
2. When the black marble is added to the graduated cylinder and it sinks, the water level should rise by an amount equal to the volume of the marble. So, the final volume indicated by the water level is the initial volume of water plus the volume of the marble.
Let's assume that the initial volume of water is x mL.
Final volume = Initial volume of water + Volume of the marble
Final volume = x mL + 2 cm^3
Since the units of volume need to be the same, we need to convert cm^3 to mL. 1 cm^3 is equal to 1 mL.
Final volume = x mL + 2 mL
Final volume = (x + 2) mL
So, the final volume indicated by the water level is (x + 2) mL (rounded to the ones place).