Question
What volume of iron of density 7.8 g/cm³ must be attached to wood whose mass is 100 g and density of 0.5 g/cm³ if both iron and wood have to be submerged in the water?
Answers
GPT 3.5
Before we can calculate the volume of iron needed to submerge both the iron and wood in water, we need to determine the volume of the wood.
Given that the mass of the wood is 100g and the density of wood is 0.5 g/cm³, we can calculate the volume of wood as follows:
Volume of wood = Mass / Density
Volume of wood = 100g / 0.5 g/cm³
Volume of wood = 200 cm³
Now, let V represent the volume of iron needed to submerge both the iron and wood in water.
The total volume of both the iron and wood when submerged in water is the sum of their volumes:
Volume of iron + Volume of wood = V
Let x represent the volume of iron needed.
Density of iron = 7.8 g/cm³
Mass of iron = Volume of iron * Density of iron
Mass of iron = x * 7.8
Since the total mass when both iron and wood are submerged in water is equal to the sum of their masses individually:
Total mass = Mass of iron + Mass of wood
Total mass = x * 7.8 + 100
Now, we know that the total volume when both iron and wood are submerged in water is equal to the sum of their volumes individually:
Volume of iron + Volume of wood = V
x + 200 = V
Since the total mass when both iron and wood are submerged in water is equal to the sum of their masses individually:
Total mass = Mass of iron + Mass of wood
Total mass = x * 7.8 + 100
Since the total mass when both iron and wood are submerged in water is equal to the sum of their masses individually, we can equate the two equations:
x * 7.8 + 100 = x + 200
7.8x + 100 = x + 200
6.8x = 100
x = 100 / 6.8
x ≈ 14.71 cm³
Therefore, approximately 14.71 cm³ of iron is needed to submerge both the iron and wood in water.
Given that the mass of the wood is 100g and the density of wood is 0.5 g/cm³, we can calculate the volume of wood as follows:
Volume of wood = Mass / Density
Volume of wood = 100g / 0.5 g/cm³
Volume of wood = 200 cm³
Now, let V represent the volume of iron needed to submerge both the iron and wood in water.
The total volume of both the iron and wood when submerged in water is the sum of their volumes:
Volume of iron + Volume of wood = V
Let x represent the volume of iron needed.
Density of iron = 7.8 g/cm³
Mass of iron = Volume of iron * Density of iron
Mass of iron = x * 7.8
Since the total mass when both iron and wood are submerged in water is equal to the sum of their masses individually:
Total mass = Mass of iron + Mass of wood
Total mass = x * 7.8 + 100
Now, we know that the total volume when both iron and wood are submerged in water is equal to the sum of their volumes individually:
Volume of iron + Volume of wood = V
x + 200 = V
Since the total mass when both iron and wood are submerged in water is equal to the sum of their masses individually:
Total mass = Mass of iron + Mass of wood
Total mass = x * 7.8 + 100
Since the total mass when both iron and wood are submerged in water is equal to the sum of their masses individually, we can equate the two equations:
x * 7.8 + 100 = x + 200
7.8x + 100 = x + 200
6.8x = 100
x = 100 / 6.8
x ≈ 14.71 cm³
Therefore, approximately 14.71 cm³ of iron is needed to submerge both the iron and wood in water.