Difference between revisions of "2022 AMC 8 Problems/Problem 24"
(→Remark) |
(→Solution 2) |
||
Line 69: | Line 69: | ||
label("$6$",midpoint(H--F),1.5*S,red); | label("$6$",midpoint(H--F),1.5*S,red); | ||
label("$8$",midpoint(H--J),1.5*W,red); | label("$8$",midpoint(H--J),1.5*W,red); | ||
+ | |||
+ | /* -._-. (edited by Lvluo .-_.- :) */ | ||
</asy> | </asy> | ||
Then the volume of this triangular prism is <math>8 \times \frac {6 \times 8}{2} = \boxed{\textbf{(C) }192}</math>. | Then the volume of this triangular prism is <math>8 \times \frac {6 \times 8}{2} = \boxed{\textbf{(C) }192}</math>. | ||
− | |||
~MRENTHUSIASM | ~MRENTHUSIASM |
Revision as of 16:13, 7 June 2022
Problem
The figure below shows a polygon , consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that
and
. What is the volume of the prism?
Solution
While imagining the folding, goes on
goes on
and
goes on
So,
and
Also,
becomes an edge parallel to
so that means
Since then
So, the area of
is
If we let
be the base, then the height is
So, the volume is
Solution by aops-g5-gethsemanea2
Solution 2
After folding polygon on the dotted lines, we obtain the following triangular prism:
Then the volume of this triangular prism is .
~MRENTHUSIASM
Video Solution
https://www.youtube.com/watch?v=2uoBPp4Kxck
~Mathematical Dexterity
Video Solution
https://youtu.be/Ij9pAy6tQSg?t=2432
~Interstigation
See Also
2022 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.