Difference between revisions of "2017 AMC 12A Problems/Problem 8"
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Revision as of 18:17, 8 February 2017
Problem
The region consisting of all points in three-dimensional space within units of line segment
has volume
. What is the length
?
Solution
Let the length be
. Then, we see that the region is just the union of the cylinder with central axis
and radius
and the two hemispheres connected to each face of the cylinder (also with radius
). Thus the volume is
See Also
2017 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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