Difference between revisions of "2021 AMC 10A Problems/Problem 13"
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| − | + | ==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> ? | ||
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| + | <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> | ||
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| + | ==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 14:16, 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 | ||
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