An object measures 12 x 3 x 2.5 cm and has a density of 0.6 g/cm3. When it
is placed in water, what is the volume of the part of the object that is above
the surface of the water?
To find the volume of the part of the object that is above the surface of the water, we need to determine the volume of the entire object and then subtract the volume of the part that is submerged.
Step 1: Calculate the volume of the entire object.
The object measures 12 x 3 x 2.5 cm. To find the volume, multiply these three dimensions together:
Volume = 12 cm * 3 cm * 2.5 cm = 90 cm3
Step 2: Calculate the volume of the submerged part.
The density of the object is given as 0.6 g/cm3, which means that for every 1 cm3 of volume, the object weighs 0.6 grams. Since the object is submerged in water, it displaces an equal volume of water. The weight of this displaced water is equal to the weight of the object itself.
To find the weight of the object, we can use the formula:
Weight = Density * Volume
Given that the density of the object is 0.6 g/cm3 and the volume of the entire object is 90 cm3, we can calculate the weight of the object:
Weight = 0.6 g/cm3 * 90 cm3 = 54 grams
Since the weight of the object is equal to the weight of the displaced water, the volume of the submerged part is equal to the weight of the object divided by the density of water.
The density of water is approximately 1 g/cm3.
Volume of submerged part = Weight of object / Density of water = 54 g / 1 g/cm3 = 54 cm3
Step 3: Calculate the volume of the part above the water surface.
To find the volume of the part above the water surface, subtract the volume of the submerged part from the volume of the entire object:
Volume of part above water = Volume of entire object - Volume of submerged part
Volume of part above water = 90 cm3 - 54 cm3 = 36 cm3
So, the volume of the part of the object that is above the surface of the water is 36 cm3.