Difference between revisions of "2021 AMC 10A Problems/Problem 13"
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==Problem== | ==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> ? | 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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~ pi_is_3.14 | ~ pi_is_3.14 | ||
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| + | ==Video Solution (Simple and Quick)== | ||
| + | https://youtu.be/bRrchiDCrKE | ||
| + | |||
| + | Education, the Study of Everything | ||
==See also== | ==See also== | ||
{{AMC10 box|year=2021|ab=A|num-b=12|num-a=14}} | {{AMC10 box|year=2021|ab=A|num-b=12|num-a=14}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 19:06, 15 February 2021
Contents
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 using the formula for the volume of a pyramid: 
, so we have an answer of 
. ~IceWolf10
Similar Problem
https://artofproblemsolving.com/wiki/index.php/2015_AMC_10A_Problems/Problem_21
Video Solution (Using Pythagorean Theorem, 3D Geometry - Tetrahedron)
~ pi_is_3.14
Video Solution (Simple and Quick)
Education, the Study of Everything
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. 
