An empty graduated cylinder has a mass of 𝟓𝟎 grams. The cylinder has a mass of 𝟏𝟐𝟎 grams when 𝟑𝟎 milliliters of water is poured into it. When a rock is added to the graduated cylinder, the water level rises to 𝟕𝟓 milliliters and the mass is 𝟐𝟓𝟎 grams. Determine the density of the rock.

To determine the density of the rock, we need to use the formula:

Density = Mass / Volume

First, let's calculate the volume of water added to the graduated cylinder. The initial volume of water added is 30 mL, and the final volume is 75 mL. Thus, the volume of water added is 75 mL - 30 mL = 45 mL.

Next, let's calculate the mass of the water added. The initial mass of the empty graduated cylinder is 50 grams, and the mass of the cylinder when 30 mL of water is added is 120 grams. So, the mass of the water added is 120 grams - 50 grams = 70 grams.

Now, let's find the mass of the rock. The mass of the graduated cylinder with water and the rock is 220 grams, while the mass of the water alone is 70 grams. Therefore, the mass of the rock is 220 grams - 70 grams = 150 grams.

Finally, we can calculate the density of the rock:

Density = Mass / Volume = 150 grams / 45 mL

To convert the volume from mL to cm³, we need to use the conversion factor:

1 mL = 1 cm³

Therefore, the density of the rock is:

Density = 150 grams / 45 cm³ = 3.33 grams/cm³

So, the density of the rock is 3.33 grams/cm³.

To determine the density of the rock, we need to use the formula:

Density = Mass / Volume

First, let's calculate the volume of water in the graduated cylinder. We know that when 30 mL of water is poured into an empty cylinder, its mass becomes 120 grams. This means that the mass of the water is 120 grams - 50 grams (mass of an empty cylinder) = 70 grams.

Therefore, the volume of water in the cylinder is 30 mL.

Next, we need to calculate the volume of the rock. We know that when the rock is added to the cylinder, the water level rises to 75 mL. So, the volume occupied by the rock is 75 mL - 30 mL = 45 mL.

Now, we have the mass of the rock, which is 230 grams (mass of the cylinder with water and the rock) - 120 grams (mass of the water) = 110 grams.

Plugging these values into the density formula, we have:

Density = Mass / Volume
Density = 110 g / 45 mL

To convert milliliters (mL) to grams (g), we need to know the density of water. The density of water is approximately 1 g/mL.

So, we can divide the volume in mL by the density of water to convert it to grams:

Density = 110 g / (45 mL / 1 g/mL)
Density = 110 g / 45 g
Density = 2.44 g/mL

Therefore, the density of the rock is 2.44 grams per milliliter.

the mass of the rock is the increase of total cylinder, water, rock mass when the rock was added

250 grams - 120 grams = 130 grams of rock
the rock volume = 75ml - 30 ml = 45 ml
so the rock density = 130/45 = 2.89 grams/ milliliter

nuts