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.
Step 1: Calculate the weight of the water displaced by the rock.
The weight of the water displaced by the rock is equal to the weight of the rock in air minus the weight of the rock in water.
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
Step 2: Calculate the volume of water displaced.
The weight of water displaced is equal to the weight of the water per unit volume times the volume of water displaced.
Weight of water displaced = Density of water * Volume of water displaced
124 lb = 62.4 lb/ft^3 * Volume of water displaced
Dividing both sides of the equation by 62.4 lb/ft^3, we get:
Volume of water displaced = 124 lb / 62.4 lb/ft^3
Volume of water displaced = 1.98 ft^3
Therefore, the volume of the rock is 1.98 ft^3.
To determine the volume of the rock, we can use Archimedes' principle, which states that the weight of the object in water is equal to the weight of the displaced water.
Step 1: Calculate the weight of the water displaced by the rock.
The weight of water displaced by the rock is the weight of the rock in air minus the weight of the rock in water.
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
Step 2: Calculate the volume of water displaced.
Since the density of fresh water is given as 62.4 lb/ft³, we can use this value to calculate the volume of water displaced.
Volume of water displaced = weight of water displaced / density of water
Volume of water displaced = 124 lb / 62.4 lb/ft³
Volume of water displaced = 1.984 ft³
Step 3: Determine the volume of the rock.
The volume of the rock is equal to the volume of water displaced because an object displaces its own volume when submerged in a fluid.
Therefore, the volume of the rock is 1.984 ft³.