All SSAT Upper Level Math Resources
Example Questions
Example Question #3 :How To Find The Volume Of A Tetrahedron
Above is the base of a triangular pyramid, which is equilateral. The height of the pyramid is equal to the perimeter of its base. In terms of, give the volume of the pyramid.
By the 30-60-90 Theorem,, or
is the midpoint of, so
The area of the triangular base is half the product of its base and its height:
The height of the pyramid is equal to the perimeter, so it will be three times, or
The volume of the pyramid is one third the product of this area and the height of the pyramid:
Example Question #4 :How To Find The Volume Of A Tetrahedron
In three-dimensional space, the four vertices of a tetrahedron - a solid with four faces - have Cartesian coordinates
,
where
Give its volume in terms of.
The tetrahedron looks like this:
is the origin andare the other three points.
This is a triangular pyramid, and we can considerthe base; its area is half the product of its legs, or
.
The volume of the tetrahedron is one third the product of its base and its height. Therefore,
After some rearrangement:
Example Question #5 :How To Find The Volume Of A Tetrahedron
In three-dimensional space, the four vertices of a tetrahedron - a solid with four faces - have Cartesian coordinates
,
where
Give its volume in terms of.
The tetrahedron looks like this:
is the origin andare the other three points, each of which lies along one of the three (mutually perpendicular) axes.
This is a triangular pyramid, and we can considerthe base; its area is half the product of its legs, or
.
The volume of the tetrahedron is one third the product of its base areaand its height. Therefore, the volume is
Example Question #6 :How To Find The Volume Of A Tetrahedron
Find the volume of a regular tetrahedron that has a side length of.
Use the following formula to find the volume of a regular tetrahedron:
Now, plug in the given side length.
Example Question #7 :How To Find The Volume Of A Tetrahedron
Find the volume of a regular tetrahedron that has a side length of.
Use the following formula to find the volume of a regular tetrahedron:
Now, plug in the given side length.
Example Question #8 :How To Find The Volume Of A Tetrahedron
Find the volume of a regular tetrahedron with a side length of.
Use the following formula to find the volume of a regular tetrahedron:
Now, plug in the given side length.
Example Question #9 :How To Find The Volume Of A Tetrahedron
Find the volume of a regular tetrahedron with side lengths of.
Use the following formula to find the volume of a regular tetrahedron:
Now, plug in the given side length.
Example Question #10 :How To Find The Volume Of A Tetrahedron
Find the volume of a regular tetrahedron with side lengths of.
Use the following formula to find the volume of a regular tetrahedron:
Now, plug in the given side length.
Example Question #11 :How To Find The Volume Of A Tetrahedron
Find the volume of a tetrahedron with side lengths of.
Use the following formula to find the volume of a regular tetrahedron:
Now, plug in the given side length.
Example Question #662 :Geometry
Find the volume of a regular tetrahedron with side lengths of.
Use the following formula to find the volume of a regular tetrahedron:
Now, plug in the given side length.
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