2021 AMC 10B Spring Problem 10

Below is the video solution and professionally curated solution for Problem 10 of the 2021 AMC 10B Spring, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 10B Spring solutions, or check the answer key.

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Concepts:volumeconecylinder

Difficulty rating: 1020

10.

An inverted cone with base radius 12cm12 \mathrm{ cm} and height 18cm18 \mathrm{ cm} is full of water. The water is poured into a tall cylinder whose horizontal base has radius of 24cm.24 \mathrm{ cm}. What is the height in centimeters of the water in the cylinder?

1.5 1.5

3 3

4 4

4.5 4.5

6 6

Video solution:
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Written solution:

The volumes must be the same since the water is poured from one to another. The volume of the cone is r2hπ3=12218π3=864π.\frac{r^2h \pi}3 = \frac{12^2\cdot 18 \pi}3 = 864 \pi.

The volume of the cylinder is r2hπ=242hπ=576hπ.r^2h \pi =24^2h \pi = 576h \pi. This makes 576hπ=864π,576 h \pi = 864 \pi, so h=1.5.h = 1.5.

Thus, the answer is A .

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