SOLUTION: Could you help me with this problem, please? I greatly appreciate your time and effort.
The cube shown has a side length of 6. Find the volume of the pyramid that has triangle B
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-> SOLUTION: Could you help me with this problem, please? I greatly appreciate your time and effort.
The cube shown has a side length of 6. Find the volume of the pyramid that has triangle B
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Question 1191007: Could you help me with this problem, please? I greatly appreciate your time and effort.
The cube shown has a side length of 6. Find the volume of the pyramid that has triangle BDE as its base and A as its vertex.
Answer by ikleyn(52803) (Show Source):
You can put this solution on YOUR website! .
Could you help me with this problem, please? I greatly appreciate your time and effort.
The cube shown has a side length of 6. Find the volume of the pyramid that has triangle BDE as its base and A as its vertex.
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Let the length of an edge of the cube be "a".
To calculate the volume, consider triangle ABE as a base of a pyramid BDEA
and edge AD as the height of the pyramid (same as its altitude).
Use the formula for the volume of a pyramide
volume = 1/3 of the base area times the height = = = = 36 cubic units.
Thus the volume of the pyramid BDEA is 1/6 of the volume of the cube = = 216 cubic units.
ANSWER. The volume of the pyramid BDEA is 36 cubic units, which is 1/6 of the volume of the cube.
Solved.
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Comment from student : Hello, I was going through your solution again and realized you are asking
to consider the triangle ABE as a base of a pyramid but the question specifies that the base of pyramid is triangle BDE.
Could you please help me taking into consideration that base is triangle BDE and not ABE?
My response : In this problem, you can consider (and can call) ANY FACE with vertex A of the pyramid BDEA as a base of the pyramid.
Then the corresponding altitude will be the edge perpendicular to this base.
