Difference between revisions of "2021 AMC 10A Problems/Problem 13"
(Created page with "The problem will be released in 115 days.") |
(added solution) |
||
Line 1: | Line 1: | ||
− | + | ==Problem== | |
+ | What is the volume of tetrahedron <math>ABCD</math> with edge lengths <math>AB = 2</math>, <math>AC = 3</math>, <math>AD = 4</math>, <math>BC = \sqrt{13}</math>, <math>BD = 2\sqrt{5}</math>, and <math>CD = 5</math> ? | ||
+ | |||
+ | <math>\textbf{(A)} ~3 \qquad\textbf{(B)} ~2\sqrt{3} \qquad\textbf{(C)} ~4\qquad\textbf{(D)} ~3\sqrt{3}\qquad\textbf{(E)} ~6</math> | ||
+ | |||
+ | ==Solution== | ||
+ | Drawing the tetrahedron out and testing side lengths, we realize that the triangles ABD and ABC are right triangles. It is now easy to calculate the volume of the tetrahedron, obtaining an answer of <math>\boxed{C}</math>. | ||
+ | |||
+ | ==See also== | ||
+ | {{AMC10 box|year=2021|ab=A|num-b=12|num-a=14}} | ||
+ | {{MAA Notice}} |
Revision as of 15:16, 11 February 2021
Problem
What is the volume of tetrahedron with edge lengths
,
,
,
,
, and
?
Solution
Drawing the tetrahedron out and testing side lengths, we realize that the triangles ABD and ABC are right triangles. It is now easy to calculate the volume of the tetrahedron, obtaining an answer of .
See also
2021 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.