2008 AMC 10B Problems/Problem 19
Problem
A cylindrical tank with radius feet and height feet is lying on its side. The tank is filled with water to a depth of feet. What is the volume of water, in cubic feet?
Video Solution(Based on Solution 1)
https://www.youtube.com/watch?v=I9RRrumPRK4
Solution
Any vertical cross-section of the tank parallel with its base looks as follows:
The volume of water can be computed as the height of the tank times the area of the shaded part.
Let be the size of the smaller angle . We then have , hence .
The figure is symmetrical, so the angle has size . Hence the shaded part consists of of the circle, minus the area of the triangle .
Using the Pythagorean theorem we can compute that . Thus , and the area of the triangle is .
The area of the shaded part is then , and the volume of water is . The answer is .
Alternatively, we can solve for DC and see it is congruent to a 30 60 90 triangle by SSS ~Williamgolly
See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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