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Question 625552: Hello, i had a question regarding volume. If you have an aquariam that measures three feet high and one foot wide, what is the rock's volume that is in the water. Also the water has rised 1/2 inch. So far i drew a shape that is 3.5 high and 1 feet wide but i am stuck after this. If anybody could please assist me I would greatly appreciate it thank!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if you knew the length of the aquarium, you could solve this easily.
assume the length is 3 feet.
your aquarium is 3 feet high 1 feet wide and 3 feet long.
the volume is 3*1*3 = 9 cubic feet.
now you put a rock in the water and the water rises by 1/2 of an inch.
1/2 of an inch is equal to 1/24 of a foot because there are 12 inches to a foot and therefore 24 1/2 inches to a foot.
so the water rises by 1/24 of a foot.
your volume is now 3+1/24 feet high, 1 feet wide, 3 feet long.
the new volume is 73/24 * 1 * 3 = 9.125 cubic feet.
the volume of the water that is displaced by the rock is equal to .125 cubic feet.
if you had a different length, you would get a different answer.
assume the length of the aquarium was 6 feet.
the original volume is now 3*1*6 = 18 cubic feet.
add 1/24 of a foot to the height and you get dimensions of 3+1/24 feet high, 1 feet wide, 6 feet long.
the new volume is 73/24 * 1 * 6 = 18.25 cubic feet.
this means the volume of the rock is equal to .25 cubic feet.
when the aquarium was 3 feet long, the volume of the water displaced by the rock was .125 cubic feet.
when the aquarium was 6 feet long, the volume of the water displaced by the rock was .25 cubic feet.
the difference was in the length of the aquarium.
since volume is equal to length * width * height, it stands to reason if the length of the aquarium is doubled, then the additional 1/2 inch in height has consumed double the volume.
1/2 inches equals 1/24 of a foot.
1/24 * 1 * 3 = 3/24
1/24 * 1 * 6 = 6/24
assuming that the rock raised the water by 1/2 inch in both cases, the same rock displaces double the volume when the length of the aquarium is doubled.
bottom line is you need the 3 dimensions to determine the volume displaced by the rock.
since you only have 2, you can't measure the volume of the rock until you know the length of the aquarium
note that if we are talking about the same rock, then the rock would have raised the height of the water only 1/4 of an inch if the length of the aquarium was 6 feet rather than 3.
that's because the volume of the rock doesn't change, so if the dimnensions of the aquarium change, then the change in height that the rock causes has to change.
rock causes a change in height of 1/2 inch when the length of the aquarium is 3 feet (assumed).
to keep the same volume, the rock would cause a change in height of 1/4 inch when the length of the aquarium is 6 feet.
73/24 * 1 * 3 = 9.125 from 3*1*3 = 9 caused a change in volume of .125 cubic feet.
145/48 * 1 * 6 = 18.125 from 3*1*6 = 18 causes a change in voolume of .125 cubic feet.
the change in volume is the same as it should be since the volume of the rock hasn't changed.
note that 73/24 is equal to 3 + 1/24 feet and 1/24 feet = 1/2 inch.
note that 145/48 i8s equal to 3 + 1/48 feet and 1/48 feet = 1/4 inch.
bottom line again:
you need the length of the aquarium to measure the volume of the rock.
that measurement is missing.
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