Problem:
An aquarium has a rectangular base that measures by and has a height of . The aquarium is filled with water to a depth of . A rock with volume is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?
Answer Choices:
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Solution:
Using the volume formula , the volume of water in the aquarium is . When the rock is put in, the water and the rock will occupy a box-shaped region with volume . The volume of the water and the rock is , where is the new height of the water. The new volume , so the new height is
After adding the rock, the water rises .
Because the shape of the rock is irrelevant, we may assume that the rock is shaped like a rectangular box with base measuring and height . Using the volume formula, , so . When the rock is put into the aquarium, the water level will rise by .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions