2021 AMC 12B Spring Problem 6

Below is the professionally curated solution for Problem 6 of the 2021 AMC 12B Spring, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 12B Spring solutions, or check the answer key.

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Concepts:cone cylinder volume

Difficulty rating: 1220

An inverted cone with base radius $12$ cm and height $18$ cm is full of water. The water is poured into a tall cylinder whose horizontal base has a radius of $24$ cm. What is the height in centimeters of the water in the cylinder?

$1.5$

$3$

$4$

$4.5$

$6$

Solution:

The cone holds $\dfrac13\pi(12)^2(18)=864\pi$ cubic centimeters of water.

Poured into the cylinder, this fills to height $h$ where $\pi(24)^2 h=864\pi.$

Then $576h=864,$ so $h=1.5.$

Thus, the correct answer is A.

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