Answer:
Explanation:
Since the two bottles are similar, we know that they have the same shape, but the larger bottle is scaled up by a certain factor compared to the smaller bottle. Let's denote this scaling factor by k.
The volume of the smaller bottle is 500 ml, so we can set up the following proportion between the volumes of the two bottles:
volume of larger bottle / volume of smaller bottle = k³
Since the scaling factor applies to all three dimensions of the bottle, we need to use k³ instead of just k. We want to solve for the volume of the larger bottle, so we can rearrange the proportion to isolate the volume of the larger bottle:
volume of larger bottle = (k³) * volume of smaller bottle
We don't know the value of k, but we do know that the bottles are similar, which means that corresponding dimensions are proportional. In particular, the ratio of corresponding lengths is k, the ratio of corresponding widths is k, and the ratio of corresponding heights is k. Therefore, we have:
k (corresponding length) = k (corresponding width) = k (corresponding height)
We also know that the smaller bottle has a volume of 500 ml, which is equivalent to 0.5 liters. We can use this information to solve for k:
0.5 liters = (1/1000) cubic meters = (k³) * (1/1000) cubic meters
Simplifying, we get:
k³ = 500/1000 = 1/2
Taking the cube root of both sides, we get:
k = (1/2)^(1/3)
Now we can substitute this value of k into the formula we derived earlier to find the volume of the larger bottle:
volume of larger bottle = ((1/2)^(1/3))³ * 500 ml
Simplifying, we get:
volume of larger bottle = (1/2) * 500 ml = 250 ml
Therefore, the larger bottle can hold 250 ml of water.