All ISEE Upper Level Math Resources
Example Questions
Example Question #1 :Tetrahedrons
A triangular pyramid, or tetrahedron, with volume 100 has four vertices with Cartesian coordinates
where.
评估.
The tetrahedron is as follows (figure not to scale):
This is a triangular pyramid with a right triangle with legs 10 andas its base; the area of the base is
The height of the pyramid is 5, so
Set this equal to 100 to get:
Example Question #2 :Tetrahedrons
A triangular pyramid, or tetrahedron, with volume 1,000 has four vertices with Cartesian coordinates
where.
评估.
The tetrahedron is as follows:
This is a triangular pyramid with a right triangle with two legs of measureas its base; the area of the base is
Since the height of the pyramid is also, the volume is
.
Set this equal to 1,000:
Example Question #3 :Tetrahedrons
A triangular pyramid, or tetrahedron, with volume 240 has four vertices with Cartesian coordinates
where.
评估.
The tetrahedron is as follows (figure not to scale):
This is a triangular pyramid with a right triangle with two legs of measureas its base; the area of the base is
The height of the pyramid is 24, so the volume is
Set this equal to 240 to get: