2004 AMC 10A Problem 19

Below is the professionally curated solution for Problem 19 of the 2004 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 10A solutions, or check the answer key.

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Concepts:cylinder net (3D geometry)parallelogram

Difficulty rating: 1600

19.

A cylindrical silo has a diameter of $30$ feet and a height of $80$ feet. A stripe with a horizontal width of $3$ feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet?

$120$

$180$

$240$

$360$

$480$

Solution:

Unrolling the stripe flattens it into a parallelogram. Its base (the horizontal width) is $3$ feet and its height spans the full $80$ feet of the silo.

The area is therefore $3 \times 80 = 240$ square feet.

Thus, the correct answer is C.

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