The density of ice is 0.92g cm-3 & that of sea water is 1.025g cm-3.Find the total volume of an iceberg which floats with its volume 800cm3 above water?
ANSWER:7809.5cm3
To find the total volume of the iceberg, we need to calculate the volume submerged in water and add it to the volume above water.
1. Calculate the volume submerged in water:
The density of sea water is 1.025 g/cm3.
Let's assume the volume submerged in water is V.
According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Therefore, the buoyant force acting on the iceberg is equal to the weight of the submerged volume of water.
The buoyant force (B) can be calculated using the formula:
B = density of sea water * g * V
Where g is the acceleration due to gravity (approximately 9.8 m/s2).
The weight of the iceberg (W) is given by:
W = density of ice * g * total volume of the iceberg
Since the iceberg is in equilibrium, the buoyant force and the weight are equal:
B = W
By substituting the values, we get:
density of sea water * g * V = density of ice * g * total volume of the iceberg
Now, solve for V:
V = (density of ice * total volume of the iceberg) / density of sea water
Plugging in the values:
V = (0.92 g/cm3 * 800 cm3) / 1.025 g/cm3
Calculating this gives:
V ≈ 712.19 cm3
2. Calculate the total volume of the iceberg:
Given that the volume above water is 800 cm3, we can now calculate the total volume of the iceberg by adding the submerged volume to the volume above water.
Total volume = submerged volume + volume above water
Total volume = V + 800 cm3
Total volume = 712.19 cm3 + 800 cm3
Calculating this gives:
Total volume ≈ 1512.19 cm3
Therefore, the total volume of the iceberg is approximately 1512.19 cm3, which can be rounded to 1512 cm3.
To find the total volume of the iceberg, we need to determine the volume of the part submerged in water. We can use the principle of buoyancy to do this.
Step 1: Determine the density of the iceberg.
Since the iceberg is floating, its density is equal to the density of the sea water. Therefore, the density of the iceberg is 1.025 g/cm³.
Step 2: Determine the volume of the submerged part.
The volume of the submerged part can be calculated using the formula:
Volume = (mass of the object) / (density of the object)
Let's assume the mass of the submerged part is m grams.
Volume of the submerged part = m / (density of the iceberg)
Step 3: Calculate the mass of the submerged part.
The mass of the submerged part can be calculated using the formula:
Mass = Density x Volume
Since the volume of the submerged part is equal to the volume above the water (800 cm³), we can calculate the mass of the submerged part:
Mass = 1.025 g/cm³ x 800 cm³
Step 4: Calculate the total volume of the iceberg.
The total volume of the iceberg can be calculated using the formula:
Total Volume = (Volume above water) + (Volume submerged)
Total Volume = 800 cm³ + (Mass of submerged part) / (density of the iceberg)
Step 5: Substitute the values and calculate.
Total Volume = 800 cm³ + (1.025 g/cm³ x 800 cm³) / (1.025 g/cm³)
Total Volume = 800 cm³ + 800 cm³
Total Volume = 1600 cm³
Therefore, the total volume of the iceberg is 1600 cm³.
Va = Vi - Vb,
Va = Vi - (Di/Dw)*Vi = 800 cm^3,
Vi - (0.92/1.025)Vi = 800,
Vi - 0.898Vi = 800,
0.102Vi = 800,
Vi = 800 / 0.102 = 7843 cm^3. = Vol. of
ice.
Va = Vol. above water.
Vb = Vol. below water.
Di = Density of ice.
Dw = Density of water.