A rectangular container is 5 cm. wide and 12 cm. long and contains water to a depth of 7 cm. A stone is placed in the water and the water rises 1.7 cm. Find the volume of the stone.
volume without the stone = 5x12x7 = 420
volume with the stone = 5x12x8.7 = 522
for an increase of 102 cm^3 , so according to Archimedes that increase would have been caused by the volume of the stone.
I agree with the answer
To find the volume of the stone, we need to calculate the change in water volume when the stone is placed in the container.
Step 1: Calculate the initial water volume:
The initial water volume is given by the formula: Volume = Length × Width × Depth
Volume = 12 cm × 5 cm × 7 cm
Volume = 420 cm³
Step 2: Calculate the final water volume:
When the stone is placed in the water, the water level rises by 1.7 cm. This means the final water depth is 7 cm + 1.7 cm = 8.7 cm.
The final water volume is given by the formula: Volume = Length × Width × Depth
Volume = 12 cm × 5 cm × 8.7 cm
Volume = 522 cm³
Step 3: Calculate the volume of the stone:
The volume of the stone can be found by subtracting the initial water volume from the final water volume.
Volume of the stone = Final water volume - Initial water volume
Volume of the stone = 522 cm³ - 420 cm³
Volume of the stone = 102 cm³
Therefore, the volume of the stone is 102 cm³.
To find the volume of the stone, we need to calculate the change in volume of water when the stone is placed in the container.
First, let's calculate the initial volume of water in the container:
Initial volume of water = width × length × depth
Initial volume of water = 5 cm × 12 cm × 7 cm
Next, let's calculate the final volume of water in the container when the stone is added:
Final volume of water = width × length × height
Final volume of water = 5 cm × 12 cm × (7 cm + 1.7 cm)
Now, to find the volume of the stone, we need to calculate the difference between the final and initial volumes of water:
Volume of stone = Final volume of water - Initial volume of water
Let's substitute the values and calculate the answer.