2021 AMC 10A Problems/Problem 13: Difference between revisions
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==Solution== | ==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: <math>\frac{3\cdot4\cdot2}{3\cdot2}=4</math>, so we have an answer of <math>\boxed{C}</math>. ~IceWolf10 | 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: <math>\frac{3\cdot4\cdot2}{3\cdot2}=4</math>, so we have an answer of <math>\boxed{C}</math>. ~IceWolf10 | ||
== Video Solution (Using Pythagorean Theorem, 3D Geometry - Tetrahedron) == | |||
https://youtu.be/i4yUaXVUWKE | |||
~ pi_is_3.14 | |||
==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 16:20, 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 using the formula for the volume of a pyramid: 
, so we have an answer of 
. ~IceWolf10
Video Solution (Using Pythagorean Theorem, 3D Geometry - Tetrahedron)
~ pi_is_3.14
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 | ||
These problems are copyrighted © by the Mathematical Association of America. 
