A rock, which weighs 350 lb in air, weighs 226 lb when submerged in fresh
water (62.4 lb/ft3). The volume of the rock is:
To find the volume of the rock, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
First, let's calculate the weight of the water displaced by the rock. The difference between the weight of the rock in air and the weight of the rock in water gives us the weight of the water displaced:
Weight of water displaced = Weight of rock in air - Weight of rock in water
Weight of water displaced = 350 lb - 226 lb
Weight of water displaced = 124 lb
Next, we can calculate the volume of the water displaced. We know that the density of water is 62.4 lb/ft³, so we can use the density formula:
Density = Mass / Volume
Volume = Mass / Density
Using the weight of water displaced (mass) and the density of water, we can find the volume:
Volume = 124 lb / (62.4 lb/ft³)
Volume = 1.98 ft³
Therefore, the volume of the rock is approximately 1.98 ft³.
To find the volume of the rock, we can use the principle of buoyancy.
The weight of an object in air is equal to the weight of the object in water displaced by it. This is known as Archimedes' principle.
In this case, the difference in weight of the rock between air and water is the weight of the water it displaces, which is equal to the buoyant force acting on it.
The weight of the rock in air is 350 lb, and the weight of the rock in water is 226 lb.
Therefore, the weight of the water displaced is 350 lb - 226 lb = 124 lb.
To find the volume of water displaced, we need to convert the weight of the water to volume using the density of water.
The density of water is given as 62.4 lb/ft³.
So, we can calculate the volume of water displaced using the formula:
Volume = Weight / Density
Volume = 124 lb / 62.4 lb/ft³ = 1.987 ft³
Hence, the volume of the rock is approximately 1.987 cubic feet.