A container has a rectangular base area of 6400 cm². It was filled with water up to a height of 1 m. Alex added 480 bottles of water, and the height of the water level rose to 2.5 m. Find the volume of each bottle of water.Volume of each bottle of water: ____ cm³.
Question
A container has a rectangular base area of 6400 cm². It was filled with water up to a height of 1 m. Alex added 480 bottles of water, and the height of the water level rose to 2.5 m. Find the volume of each bottle of water.Volume of each bottle of water: ____ cm³.
Solution
To solve this problem, we need to find the volume of the water added by Alex.
Step 1: Convert the height of the water level from meters to centimeters because the base area is given in cm². 1 m = 100 cm, so 2.5 m = 250 cm.
Step 2: Find the volume of the water in the container before and after Alex added the bottles. The volume of a rectangular prism (which is what the container is) is found by multiplying the length by the width by the height. In this case, we don't know the length and the width separately, but we do know that their product is 6400 cm² (the base area). So, the volume before Alex added the bottles is 6400 cm² * 100 cm = 640,000 cm³. The volume after he added the bottles is 6400 cm² * 250 cm = 1,600,000 cm³.
Step 3: Subtract the initial volume from the final volume to find the volume of the water added by Alex. 1,600,000 cm³ - 640,000 cm³ = 960,000 cm³.
Step 4: Divide the volume of the water added by the number of bottles to find the volume of each bottle. 960,000 cm³ / 480 bottles = 2000 cm³/bottle.
So, the volume of each bottle of water is 2000 cm³.
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