2007 AMC 10A Problem 3

Below is the professionally curated solution for Problem 3 of the 2007 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 10A solutions, or check the answer key.

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Concepts:volume rectangular prism

Difficulty rating: 960

An aquarium has a rectangular base that measures $100$ cm by $40$ cm and has a height of $50$ cm. It is filled with water to a height of $40$ cm. A brick with a rectangular base that measures $40$ cm by $20$ cm and a height of $10$ cm is placed in the aquarium. By how many centimeters does the water rise?

$0.5$

$1$

$1.5$

$2$

$2.5$

Solution:

The brick has volume $40 \cdot 20 \cdot 10 = 8000$ cubic centimeters.

If the water rises by $h$ centimeters, the added volume is $100 \cdot 40 \cdot h = 4000h$ cubic centimeters.

Setting these equal gives $4000h = 8000,$ so $h = 2.$

Thus, the correct answer is D.

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